Wormhole lecture. Astrophysicists are seriously looking for “wormholes” in space

The science

The recently released visually arresting film Inresttellar is based on real scientific concepts such as rotating black holes, wormholes and time dilation.

But if you are not familiar with these concepts, you may be a little confused while watching.

In the film, a team of space explorers goes to extragalactic travel through a wormhole. On the other side, they find themselves in a different solar system with a rotating black hole instead of a star.

They are in a race against space and time to complete their mission. This kind of space travel may seem a little confusing, but it is based on basic principles of physics.

Here are the main ones 5 concepts of physics Things you need to know to understand Interstellar:

Artificial gravity

The biggest problem we humans face during long-term space travel is weightlessness. We were born on Earth and our bodies have adapted to certain gravitational conditions, but when we are in space for a long time, our muscles begin to weaken.

The characters in the movie Interstellar also face this problem.

To cope with this, scientists are creating artificial gravity in spacecraft. One way to do this is to spin up the spaceship, just like in the movie. The rotation creates a centrifugal force that pushes objects toward the outer walls of the ship. This repulsion is similar to gravity, only in the opposite direction.

This is a form of artificial gravity you experience when you are driving around a small radius curve and feel as if you are being pushed outward, away from the center point of the curve. In a spinning spaceship, the walls become your floor.

Rotating black hole in space

Astronomers, albeit indirectly, have observed in our Universe rotating black holes. Nobody knows what's at the center of a black hole, but scientists have a name for it -singularity .

Rotating black holes distort the space around them differently than stationary black holes.

This distortion process is called "inertial frame entrainment" or the Lense-Thirring effect, and it affects how the black hole will look by distorting space, and more importantly the space-time around it. The black hole you see in the movie is enoughvery close to the scientific concept.

• The spaceship Endurance is heading towards Gargantua - fictional supermassive black hole with a mass 100 million times greater than the Sun.
• It is 10 billion light years away from Earth and has several planets orbiting it. Gargantua spins at an astonishing 99.8 percent of the speed of light.
• Garagantua's accretion disk contains gas and dust with the temperature of the Sun's surface. The disk supplies the Gargantua planets with light and heat.

The complex appearance of the black hole in the film is due to the fact that the image of the accretion disk is distorted by gravitational lensing. Two arcs appear in the image: one formed above the black hole, and the other below it.

Mole Hole

The wormhole or wormhole used by the crew in Interstellar is one of the phenomena in the film that whose existence has not been proven. It is hypothetical, but very convenient in the plots of science fiction stories where you need to overcome a large space distance.

Just wormholes are a kind of shortest path through space. Any object with mass creates a hole in space, which means space can be stretched, warped, and even folded.

A wormhole is like a fold in the fabric of space (and time) that connects two very distant regions, which helps space travelers travel a long distance in a short period of time.

The official name for a wormhole is an “Einstein-Rosen bridge,” as it was first proposed by Albert Einstein and his colleague Nathan Rosen in 1935.

• In 2D diagrams, the mouth of a wormhole is shown as a circle. However, if we could see the wormhole, it would look like a sphere.
• On the surface of the sphere, a gravitationally distorted view of space on the other side of the “hole” would be visible.
• The dimensions of the wormhole in the film: 2 km in diameter and the transfer distance is 10 billion light years.

Gravitational time dilation

Gravitational time dilation is a real phenomenon observed on Earth. It arises because time is relative. This means that it flows differently for different coordinate systems.

When you are in a strong gravitational environment, time moves slower for you compared to people in a weak gravitational environment.

WORMHOLE - 1) astrophysics. The most important concept of modern astrophysics and practical cosmology. A “wormhole” or “wormhole” is a transdimensional passage connecting a black hole and its corresponding white hole.

An astrophysical wormhole pierces the folded space in extra dimensions and allows one to travel along a truly short path between star systems.

Research using the Hubble Space Telescope has shown that every black hole is the entrance to a wormhole (see HUBBLE'S LAW). One of the largest holes is located in the center of our Galaxy. It was shown theoretically (1993) that it was from this central hole that the Solar System arose.

According to modern concepts, the observable part of the Universe is literally all riddled with “wormholes” going “back and forth.” Many prominent astrophysicists believe that travel through “wormholes” is the future of interstellar astronautics. "

We are all accustomed to the fact that we cannot return the past, although sometimes we really want to. For more than a century, science fiction writers have been depicting various kinds of incidents that arise due to the ability to travel through time and influence the course of history. Moreover, this topic turned out to be so pressing that at the end of the last century, even physicists far from fairy tales began to seriously search for solutions to the equations describing our world that would make it possible to create time machines and overcome any space and time in the blink of an eye.

Science fiction novels describe entire transport networks connecting star systems and historical eras. He stepped into a booth stylized, say, as a telephone booth, and found himself somewhere in the Andromeda nebula or on Earth, but visiting the long-extinct tyrannosaurs.

Characters in such works constantly use time machine null-transportation, portals and similar convenient devices.

However, science fiction fans perceive such travels without much trepidation - you never know what one can imagine, attributing the implementation of an idea to an uncertain future or to the insights of an unknown genius. What is much more surprising is that time machines and tunnels in space are quite seriously, as hypothetically possible, actively discussed in articles on theoretical physics, on the pages of the most reputable scientific publications.

The answer lies in the fact that, according to Einstein's theory of gravity - the general theory of relativity (GTR), the four-dimensional space-time in which we live is curved, and the familiar gravity is a manifestation of such curvature.

Matter “bends”, bends the space around itself, and the denser it is, the stronger the curvature.

Numerous alternative theories of gravity, numbering in the hundreds, differ from GTR in detail, but retain the main thing - the idea of ​​​​the curvature of space-time. And if space is curved, then why shouldn’t it take, for example, the shape of a pipe, short-circuiting regions separated by hundreds of thousands of light years, or, say, eras far from each other - after all, we are talking not just about space, but about space- time?

Remember, from the Strugatskys (who, by the way, also resorted to zero-transportation): “I don’t see at all why the noble don doesn’t...” - well, let’s say, not fly to the 32nd century?...

Wormholes or black holes?

Thoughts about such a strong curvature of our space-time arose immediately after the appearance of General Relativity - already in 1916, the Austrian physicist L. Flamm discussed the possibility of the existence of spatial geometry in the form of a kind of hole connecting two worlds. In 1935, A. Einstein and mathematician N. Rosen drew attention to the fact that the simplest solutions of the general relativity equations, which describe isolated, neutral or electrically charged sources of the gravitational field, have a spatial structure of a “bridge”, almost smoothly connecting two universes - two identical, almost flat, space-time.

This kind of spatial structures later received the name “wormholes” (a fairly loose translation of the English word “wormhole”).

Einstein and Rosen even considered the possibility of using such “bridges” to describe elementary particles. In fact, the particle in this case is a purely spatial formation, so there is no need to specially model the source of mass or charge, and with the microscopic dimensions of the wormhole, an external, remote observer located in one of the spaces sees only a point source with a certain mass and charge.

Electrical lines of force enter the hole from one side and exit from the other, without starting or ending anywhere.

In the words of the American physicist J. Wheeler, the result is “mass without mass, charge without charge.” And in this case, it is not at all necessary to assume that the bridge connects two different universes - no worse is the assumption that both “mouths” of the wormhole go out into the same universe, but at different points and at different times - something like a hollow “handle” sewn to the familiar, almost flat world.

One mouth, into which the field lines enter, can be seen as a negative charge (for example, an electron), the other, from which they exit, as a positive charge (positron), and the masses will be the same on both sides.

Despite the attractiveness of such a picture, it (for many reasons) did not take root in elementary particle physics. It is difficult to attribute quantum properties to Einstein-Rosen “bridges,” and without them there is nothing to do in the microcosm.

For known values ​​of the masses and charges of particles (electrons or protons), the Einstein-Rosen bridge does not form at all; instead, the “electric” solution predicts the so-called “bare” singularity - the point at which the curvature of space and the electric field become infinite. The concept of space-time, even if curved, loses its meaning at such points, since it is impossible to solve equations with infinite terms. General relativity itself quite clearly states where exactly it stops working. Let us remember the words said above: “connecting in an almost smooth way...”. This “almost” refers to the main flaw of the Einstein-Rosen “bridges” - a violation of smoothness in the narrowest place of the “bridge”, at the neck.

And this violation, it must be said, is very non-trivial: at such a neck, from the point of view of a remote observer, time stops...

According to modern concepts, what Einstein and Rosen considered to be the neck (that is, the narrowest point of the “bridge”) is in fact nothing more than the event horizon of a black hole (neutral or charged).

Moreover, from different sides of the “bridge” particles or rays fall on different “sections” of the horizon, and between, relatively speaking, the right and left parts of the horizon there is a special non-static area, without crossing which it is impossible to pass through the hole.

For a remote observer, a spaceship approaching the horizon of a sufficiently large (compared to the ship) black hole seems to freeze forever, and signals from it arrive less and less often. On the contrary, according to the ship's clock, the horizon is reached in a finite time.

Having passed the horizon, the ship (particle or ray of light) soon inevitably runs into a singularity - where the curvature becomes infinite and where (still on the way) any extended body will inevitably be crushed and torn apart.

This is the harsh reality of the inner workings of a black hole. The solutions of Schwarzschild and Reisner-Nordström, describing spherically symmetric neutral and electrically charged black holes, were obtained in 1916-1917, but physicists fully understood the complex geometry of these spaces only at the turn of the 1950s-1960s. By the way, it was then that John Archibald Wheeler, known for his work in nuclear physics and the theory of gravity, proposed the terms “black hole” and “wormhole.”

As it turned out, there really are wormholes in the Schwarzschild and Reisner-Nordström spaces. From the point of view of a distant observer, they are not completely visible, like the black holes themselves, and are just as eternal. But for a traveler who dares to penetrate beyond the horizon, the hole collapses so quickly that neither a ship, nor a massive particle, nor even a ray of light can fly through it.

In order to bypass the singularity and break through “to the light of God” - to the other mouth of the hole, it is necessary to move faster than light. And physicists today believe that superluminal speeds of movement of matter and energy are impossible in principle.

Wormholes and time loops

So, a Schwarzschild black hole can be viewed as an impenetrable wormhole. The Reisner-Nordström black hole is more complex, but also impassable.

However, it is not so difficult to invent and describe traversable four-dimensional wormholes by selecting the desired type of metric (a metric, or metric tensor, is a set of quantities with the help of which four-dimensional distances-intervals between point-events are calculated, which fully characterizes the geometry of space-time, and gravitational field). Passable wormholes, in general, are geometrically even simpler than black holes: there should not be any horizons leading to cataclysms with the passage of time.

Time at different points can, of course, move at different rates - but it should not endlessly speed up or stop.

It must be said that various black holes and wormholes are very interesting micro-objects that arise by themselves, like quantum fluctuations of the gravitational field (at lengths of the order of 10-33 cm), where, according to existing estimates, the concept of classical, smooth space-time is no longer applicable.

At such a scale, there should be something similar to water or soap foam in a turbulent stream, constantly “breathing” due to the formation and collapse of small bubbles. Instead of calm empty space, we have mini-black holes and wormholes of the most bizarre and intertwined configurations appearing and disappearing at a frantic pace. Their sizes are unimaginably small - they are as many times smaller than the atomic nucleus as this nucleus is smaller than the planet Earth. There is no strict description of space-time foam yet, since a consistent quantum theory of gravity has not yet been created, but in general terms the picture described follows from the basic principles of physical theory and is unlikely to change.

However, from the point of view of interstellar and intertemporal travel, wormholes of completely different sizes are needed: “I would like” for a reasonable-sized spaceship or at least a tank to pass through the neck without damage (without it, it would be uncomfortable among the tyrannosaurs, wouldn’t it?).

Therefore, first we need to obtain solutions to the gravity equations in the form of traversable wormholes of macroscopic dimensions. And if we assume that such a hole has already appeared, and the rest of space-time remains almost flat, then, consider, everything is there - the hole can be a time machine, and an intergalactic tunnel, and even an accelerator.

Regardless of where and when one of the mouths of a wormhole is located, the second can appear anywhere in space and at any time - in the past or in the future.

In addition, the mouth can move at any speed (within light speed) in relation to the surrounding bodies - this will not interfere with the exit from the hole into the (almost) flat Minkowski space.

It is known to be unusually symmetrical and looks the same at all its points, in all directions and in any inertial systems, no matter what speeds they move.

But, on the other hand, having assumed the existence of a time machine, we are immediately faced with a whole “bouquet” of paradoxes such as - flew into the past and “killed grandfather with a shovel” before grandfather could become a father. Normal common sense dictates that this, most likely, simply cannot happen. And if a physical theory claims to describe reality, it must contain a mechanism that prohibits the formation of such “time loops”, or at least make their formation extremely difficult.

GTR, without a doubt, claims to describe reality. It found many solutions that describe spaces with closed time loops, but they, as a rule, for one reason or another are considered either unrealistic or, so to speak, “harmless.”

Thus, a very interesting solution to Einstein’s equations was indicated by the Austrian mathematician K. Gödel: this is a homogeneous stationary universe, rotating as a whole. It contains closed trajectories, traveling along which you can return not only to the starting point in space, but also to the starting point in time. However, calculations show that the minimum time extent of such a loop is much greater than the existence of the Universe.

Passable wormholes, considered as "bridges" between different universes, are temporary (as we have already said) to assume that both mouths open into the same universe, as loops arise immediately. What then, from the point of view of general relativity, prevents their formation - at least on a macroscopic and cosmic scale?

The answer is simple: the structure of Einstein's equations. On their left side there are quantities that characterize space-time geometry, and on the right side there is the so-called energy-momentum tensor, which contains information about the energy density of matter and various fields, about their pressure in different directions, about their distribution in space and about state of movement.

One can "read" Einstein's equations from right to left, saying that with their help matter "tells" space how to bend. But it is also possible - from left to right, then the interpretation will be different: geometry dictates the properties of matter that could provide it, geometry, with existence.

So, if we need the geometry of a wormhole, let’s substitute it into Einstein’s equations, analyze it and find out what kind of matter is required. It turns out that it is very strange and unprecedented; it is called “exotic matter”. Thus, to create the simplest wormhole (spherically symmetrical), it is necessary that the energy density and pressure in the radial direction add up to a negative value. Need I say that for ordinary types of matter (as well as many known physical fields) both of these quantities are positive?..

Nature, as we see, has indeed put a serious barrier to the emergence of wormholes. But that’s just how humans are, and scientists are no exception: if a barrier exists, there will always be people who want to overcome it...

The work of theorists interested in wormholes can be divided into two complementary directions. The first, presupposing the existence of wormholes, considers the resulting consequences, the second tries to determine how and from what wormholes can be built, under what conditions they appear or can appear.

In the works of the first direction, for example, such a question is discussed.

Suppose we have a wormhole at our disposal, through which we can pass in a matter of seconds, and let its two funnel-shaped mouths “A” and “B” be located close to each other in space. Is it possible to turn such a hole into a time machine?

American physicist Kip Thorne and his colleagues showed how to do this: the idea is to leave one of the mouths, “A,” in place, and the other, “B” (which should behave like an ordinary massive body), accelerate to speed comparable to the speed of light, and then return back and slow down next to “A”. Then, due to the STR effect (time slowdown on a moving body compared to a stationary body), less time will pass for the mouth “B” than for the mouth “A”. Moreover, the greater the speed and duration of travel of the mouth of “B”, the greater the time difference between them.

This is, in fact, the same “twin paradox”, well known to scientists: a twin who returns from a flight to the stars turns out to be younger than his stay-at-home brother... Let the time difference between the mouths be, for example, six months.

Then, sitting near the mouth of “A” in the middle of winter, we will see through the wormhole a bright picture of the past summer and - in reality, we will return to this summer, passing right through the hole. Then we will again approach funnel “A” (it, as we agreed, is somewhere nearby), dive into the hole again and jump straight into last year’s snow. And so on as many times as you like. Moving in the opposite direction - diving into funnel “B” - let’s jump six months into the future...

Thus, having made a single manipulation with one of the mouths, we get a time machine that can be “used” constantly (assuming, of course, that the hole is stable or that we are able to maintain its “operability”).

The works of the second direction are more numerous and, perhaps, even more interesting. This direction includes the search for specific models of wormholes and the study of their specific properties, which, in general, determine what can be done with these holes and how to use them.

Exomatter and dark energy

The exotic properties of matter that the building material for wormholes must have, as it turns out, can be realized through the so-called vacuum polarization of quantum fields.

This conclusion was recently reached by Russian physicists Arkady Popov and Sergei Sushkov from Kazan (together with David Hochberg from Spain) and Sergei Krasnikov from the Pulkovo Observatory. And in this case, the vacuum is not emptiness at all, but a quantum state with the lowest energy - a field without real particles. Pairs of “virtual” particles constantly appear in it, which again disappear before they could be detected by instruments, but leave their very real trace in the form of some energy-momentum tensor with unusual properties.

And although the quantum properties of matter manifest themselves mainly in the microcosm, the wormholes they generate (under certain conditions) can reach very decent sizes. By the way, one of S. Krasnikov’s articles has a “frightening” title - “The Threat of Wormholes.” The most interesting thing in this purely theoretical discussion is that real astronomical observations in recent years seem to greatly undermine the position of opponents of the possibility of the very existence of wormholes.

Astrophysicists, studying the statistics of supernova explosions in galaxies billions of light years away from us, have concluded that our Universe is not just expanding, but is scattering at an ever-increasing speed, that is, with acceleration. Moreover, over time this acceleration even increases. This is evidenced quite confidently by the latest observations carried out on the latest space telescopes. Well, now is the time to remember the connection between matter and geometry in General Relativity: the nature of the expansion of the Universe is tightly connected with the equation of state of matter, in other words, with the relationship between its density and pressure. If the matter is ordinary (with positive density and pressure), then the density itself falls over time, and the expansion slows down.

If the pressure is negative and equal in magnitude, but opposite in sign to the energy density (then their sum = 0), then such density is constant in time and space - this is the so-called cosmological constant, which leads to expansion with constant acceleration.

But for acceleration to increase over time, and this is not enough, the sum of pressure and energy density must be negative. No one has ever observed such matter, but the behavior of the visible part of the Universe seems to signal its presence. Calculations show that such strange, invisible matter (called “dark energy”) in the present era should be about 70%, and this proportion is constantly increasing (unlike ordinary matter, which loses density with increasing volume, dark energy behaves paradoxically - the Universe is expanding, and its density is increasing). But (and we have already talked about this) it is precisely such exotic matter that is the most suitable “building material” for the formation of wormholes.

It’s tempting to fantasize: sooner or later dark energy will be discovered, scientists and technologists will learn to condense it and build wormholes, and then it won’t be long before “dreams come true” - about time machines and tunnels leading to the stars...

True, the estimate of the density of dark energy in the Universe, which ensures its accelerated expansion, is somewhat discouraging: if dark energy is distributed evenly, the result is a completely insignificant value - about 10-29 g/cm3. For an ordinary substance, this density corresponds to 10 hydrogen atoms per 1 m3. Even interstellar gas is several times denser. So if this path to creating a time machine can become real, it will not be very, very soon.

Need a donut hole

So far we have been talking about tunnel-shaped wormholes with smooth necks. But GTR also predicts another type of wormhole - and in principle they do not require any distributed matter at all. There is a whole class of solutions to Einstein’s equations, in which four-dimensional space-time, flat far from the field source, exists as if in two copies (or sheets), and the only things common to both of them are a certain thin ring (field source) and a disk, this ring limited.

This ring has a truly magical property: you can “wander” around it for as long as you like, remaining in “your” world, but if you go through it, you will find yourself in a completely different world, although similar to “yours.” And in order to return back, you need to go through the ring again (and from any side, not necessarily from the one from which you just left).

The ring itself is singular - the curvature of space-time on it goes to infinity, but all the points inside it are completely normal, and a body moving there does not experience any catastrophic effects.

It is interesting that there are a great many such solutions - both neutral, and with an electric charge, and with rotation, and without it. This, in particular, is the famous solution of the New Zealander R. Kerr for a rotating black hole. It most realistically describes black holes of stellar and galactic scales (the existence of which most astrophysicists no longer doubt), since almost all celestial bodies experience rotation, and during compression the rotation only accelerates, especially during collapse into a black hole.

So, it turns out that it is rotating black holes that are “direct” candidates for “time machines”? However, black holes that form in star systems are surrounded and filled with hot gas and harsh, deadly radiation. In addition to this purely practical objection, there is also a fundamental one related to the difficulties of moving out from under the event horizon onto a new space-time “sheet”. But this is not worth dwelling on in more detail, since according to general relativity and many of its generalizations, wormholes with singular rings can exist without any horizons.

So there are at least two theoretical possibilities for the existence of wormholes connecting different worlds: the wormholes could be smooth and composed of exotic matter, or they could arise due to a singularity while remaining traversable.

Space and strings

Thin singular rings resemble other unusual objects predicted by modern physics - cosmic strings, which were formed (according to some theories) in the early Universe when superdense matter cooled and changed its states.

They really resemble strings, only unusually heavy - many billions of tons per centimeter of length with a thickness of a fraction of a micron. And, as was shown by the American Richard Gott and the Frenchman Gerard Clement, from several strings moving relative to each other at high speeds, it is possible to create structures containing temporary loops. That is, by moving in a certain way in the gravitational field of these strings, you can return to the starting point before you left it.

Astronomers have been looking for this kind of space objects for a long time, and today there is already one “good” candidate - the object CSL-1. These are two surprisingly similar galaxies, which in reality are probably one, only bifurcated due to the effect of gravitational lensing. Moreover, in this case, the gravitational lens is not spherical, but cylindrical, resembling a long thin heavy thread.

Will the fifth dimension help?

In the event that space-time contains more than four dimensions, the architecture of wormholes acquires new, previously unknown possibilities.

Thus, in recent years the concept of a “brane world” has gained popularity. It assumes that all observable matter is located on some four-dimensional surface (denoted by the term “brane” - a truncated word for “membrane”), and in the surrounding five or six-dimensional volume there is nothing except the gravitational field. The gravitational field on the brane itself (and this is the only one we observe) obeys the modified Einstein equations, and they contain a contribution from the geometry of the surrounding volume.

So, this contribution can play the role of exotic matter that generates wormholes. Burrows can be of any size and at the same time do not have their own gravity.

This, of course, does not exhaust all the variety of “designs” of wormholes, and the general conclusion is that despite all the unusualness of their properties and despite all the difficulties of a fundamental, including philosophical, nature to which they can lead, their possible existence is worth be treated with complete seriousness and due attention.

For example, it cannot be ruled out that large holes exist in interstellar or intergalactic space, if only because of the concentration of that very dark energy that accelerates the expansion of the Universe.

There is no clear answer to the questions - what they might look like to an earthly observer and whether there is a way to detect them. Unlike black holes, wormholes may not even have any noticeable attractive field (repulsion is also possible), and therefore, one should not expect noticeable concentrations of stars or interstellar gas and dust in their vicinity.

But assuming that they can “short-circuit” regions or epochs far from each other, passing the radiation of luminaries through themselves, it is quite possible to expect that some distant galaxy will seem unusually close.

Due to the expansion of the Universe, the further away the galaxy is, the greater the spectrum shift (towards the red) its radiation comes to us. But when looking through a wormhole, there may not be a redshift. Or it will be, but something else. Some such objects can be observed simultaneously in two ways - through the hole or in the “usual” way, “past the hole”.

Thus, a sign of a cosmic wormhole could be the following: the observation of two objects with very similar properties, but at different apparent distances and at different redshifts.

If wormholes are nevertheless discovered (or built), the area of ​​philosophy that deals with the interpretation of science will face new and, it must be said, very difficult tasks. And for all the seeming absurdity of time loops and the complexity of the problems associated with causality, this field of science, in all likelihood, will somehow sort it all out sooner or later. Just as I once “coped” with the conceptual problems of quantum mechanics and Einstein’s theory of relativity...

Kirill Bronnikov, Doctor of Physical and Mathematical Sciences

21:11 09/11/2018

👁 1 719

This text represents the third version of my book about wormholes and. I tried to make it understandable for the widest possible range of readers. Understanding the material does not require special education from the reader; the most general ideas from a high school course and cognitive curiosity will be quite enough. The text does not contain formulas and does not contain complex concepts. To make things easier to understand, I have tried to use explanatory illustrations where possible. This version has been supplemented with new sections and illustrations. Corrections, clarifications and clarifications were also made to the text. If any section of the book seems boring or incomprehensible to the reader, then it can be skipped while reading without much damage to understanding.

What is commonly called a “Wormhole” in astrophysics

In recent years, many reports have appeared in the media about the discovery by scientists of certain hypothetical objects called “wormholes.” Moreover, there are even ridiculous reports of observational detection of such objects. I even read in the tabloids about the practical use of certain “wormholes”. Unfortunately, most of these reports are very far from the truth; moreover, even the concept of such “wormholes” often has nothing in common with what is commonly called “wormholes” in astrophysics.

All this prompted me to write a popular (and at the same time reliable) presentation of the theory of “wormholes” in astrophysics. But first things first.

First a little history:

The science-based theory of wormholes originated in astrophysics back in 1935 with the pioneering work of Einstein and Rosen. But in that pioneering work, the “wormhole” was called by the authors a “bridge” between different parts of the Universe (the English term is “bridge”). For a long time, this work did not arouse much interest among astrophysicists.

But in the 90s of the last century, interest in such objects began to return. First of all, the return of interest was associated with a discovery in cosmology, but I will tell you why and what the connection is a little later.

The English-language term that has taken root for “wormholes” since the 90s has become “wormhole,” but the first to propose this term back in 1957 were American astrophysicists Mizner and Wheeler (this is the same Wheeler who is considered the “father” of American hydrogen bombs). “wormhole” is translated into Russian as “worm hole.” Many Russian-speaking astrophysicists did not like this term, and in 2004 it was decided to hold a vote on various proposed terms for such objects. Among the suggested terms were: “wormhole”, “wormhole”, “wormhole”, “bridge”, “wormhole”, “tunnel”, etc. Russian-speaking astrophysicists who have scientific publications on this topic (including me) took part in the voting. As a result of this vote, the term “wormhole” won, and henceforth I will write this term without quotes.

1. So what is commonly called a wormhole?

In astrophysics, wormholes have a clear mathematical definition, but here (due to its complexity) I will not give it, and for the unprepared reader I will try to give the definition in simple words.

You can give different definitions to wormholes, but what is common to all definitions is the property that a wormhole must connect two non-curved regions of space. The junction is called a wormhole, and its central section is called the neck of the wormhole. The space near the neck of the wormhole is quite strongly curved. The concepts of “uncurved” or “curved” require detailed explanation here. But I will not explain this now, and I ask the reader to be patient until the next section, in which I will explain the essence of these concepts.

A wormhole can connect either two different universes, or the same universe in different parts. In the latter case, the distance through the wormhole (between its entrances) may be shorter than the distance between the entrances measured from the outside (although this is not at all necessary).

Further, I will use the word “universe” (with a small letter) to refer to the part of space-time that is limited by the entrances to wormholes and black holes, and the word “Universe” (with a capital letter) will mean all space-time, not anything limited.

Strictly speaking, the concepts of time and distance in curved space-time cease to be absolute values, i.e. as we subconsciously have always been accustomed to consider them. But I give these concepts a completely physical meaning: we are talking about proper time, measured by an observer who moves freely (without rocket or any other engines) almost at the speed of light (theorists usually call him an ultra-relativistic observer).

Obviously, it is practically impossible to create such an observer technically, but acting in the spirit of Einstein, we can imagine a thought experiment in which the observer saddles a photon (or other ultra-relativistic particle) and moves on it along the shortest trajectory (like Baron Munchausen on a nucleus).

Here it is worth recalling that the photon moves along the shortest path by definition; such a path is called the zero geodesic line in the general theory of relativity. In ordinary uncurved space, two points can only be connected by one zero geodesic line. In the case of a wormhole connecting entrances in the same universe, there can be at least two such paths for a photon (and both are shortest, but unequal), and one of these paths passes through the wormhole, and the other does not.

Well, it seems like I gave a simplified definition for a wormhole in simple human words (without using mathematics). However, it is worth mentioning that wormholes through which light and other matter can pass in both directions are called traversable wormholes (from now on I will simply call them wormholes). Based on the word “passable,” the question arises: are there impassable wormholes? Yes, I have. These are objects that externally (at each of the inputs) are like a black hole, but inside such a black hole there is no singularity (in physics, a singularity is an infinite density of matter that tears apart and destroys any other matter falling into it). Moreover, the property of singularity is mandatory for ordinary black holes. And the black hole itself is determined by the presence of a surface (sphere), from under which even light cannot escape. This surface is called the black hole horizon (or event horizon).

Thus, matter can get inside an impenetrable wormhole, but cannot leave it (very similar to the property of a black hole). Moreover, there may also be semi-passable wormholes, in which matter or light can only pass through the wormhole in one direction, but cannot pass in the other.

2. Curvature tunnel? Curvature of what?

At first glance, creating a wormhole tunnel from a curved space seems quite attractive. But when you think about it, you begin to come to absurd conclusions.
If you are in this tunnel, what walls can prevent you from escaping from it in the transverse direction?

And what are these walls made of?

Can empty space really prevent us from passing through them?
Or is it not empty?

In order to understand this (I don’t even suggest imagining it), let’s consider space that is not curved by gravity. Let the reader consider that this is an ordinary space with which he is always accustomed to deal and in which he lives. In what follows I will call such a space flat.

Figure 1. (original drawing by the author)
Schematic representation of the curvature of two-dimensional space. The numbers indicate successive stages of transition: from the stage of uncurved space (1) to the stage of a two-dimensional wormhole (7).

Let's take as a beginning some point “O” in this space and draw a circle around it - see figure No. 1 in Figure 1. Let both this point and this circle lie on some plane in our flat space. As we all know very well from the school mathematics course, the ratio of the length of this circle to the radius is equal to 2π, where the number π = 3.1415926535.... Moreover: the ratio of the change in the circumference to the corresponding change in the radius will also be equal to 2π (hereinafter, for brevity, we will just say ATTITUDE).

Now let’s place some body with mass M at our point “O”. If we believe Einstein’s theory and experiments (which were repeatedly carried out both on Earth and in the solar system), then space-time around the body will be curved and the above-mentioned RATIO will be less than 2π. Moreover, the larger the mass M, the smaller it is – see figures No. 2 – 4 in Figure 1. This is the curvature of space! But not only space is curved, time is also curved, and it is more correct to say that all space-time is curved, because in the theory of relativity, one cannot exist without the other - there is no clear boundary between them.

In what direction is it bent? - you ask.
Down (under the plane) or vice versa - up?

The correct answer is that the curvature will be the same for any plane drawn through the point “O”, and the direction has nothing to do with it. The very geometric property of space changes so that the ratio of the circumference to the radius also changes! Some scientists believe that the curvature of space occurs in the direction of a new (fourth) dimension. But the theory of relativity itself does not need an additional dimension; three spatial and one time dimensions are enough for it. Usually the time dimension is assigned an index of zero, and space-time is designated as 3+1.
How severe will this curvature be?

For a circle that is our equator, the relative decrease in RATIO will be 10-9, i.e. for the Earth (length of the equator)/(radius of the Earth) ≈ 2π (1 – 10-9)!!! This is such an insignificant addition. But for a circle that is the equator, this decrease is already about 10-5, and although this is also very small, modern instruments easily measure this value.

But there are more exotic objects in space than just planets and stars. For example, pulsars, which are neutron stars (composed of neutrons). The gravity on the surface of pulsars is monstrous, and their average matter density is about 1014 g/cm3 - incredibly heavy matter! For pulsars, the decrease in this RATIO is already about 0.1!

But for black holes and wormholes the decrease in this RATIO reaches unity, i.e. the ATTITUDE itself reaches zero! This means that when moving towards the center, the circumference does not change near the horizon or neck. The area of ​​the sphere around black holes or wormholes also does not change. Strictly speaking, for such objects the usual definition of length is no longer suitable, but this does not change the essence. Moreover, for a spherically symmetrical wormhole the situation does not depend on the direction from which we move towards the center.

How can you imagine this?

If we consider a wormhole, this means that we have reached a sphere of minimum area Smin=4π rmin2 with throat radius rmin. This sphere of minimal area is called the neck of the wormhole. With further movement in the same direction, we find that the area of ​​the sphere begins to increase - this means that we have passed the neck, moved into another space and are moving away from the center.

What happens if the dimensions of the falling body exceed the dimensions of the neck?

To answer this question, let's turn to a two-dimensional analogy - see Figure 2.

Let's assume that the body is a two-dimensional figure (a design cut out of paper or other material), and this design slides along a surface that is a funnel (like the one we have in a bathtub when water flows into it). Moreover, our drawing slides in the direction of the neck of the funnel so that it is pressed against the surface of the funnel with its entire surface. It is obvious that as the design approaches the neck, the curvature of the surface of the funnel increases, and the surface of the design begins to deform in accordance with the shape of the funnel at a given place in the design. Our drawing (even though it is paper), just like any physical body, has elastic properties that prevent its deformation.

At the same time, the material of the design has a physical effect on the material from which the funnel is made. We can say that both the funnel and the drawing exert elastic forces on each other.

1. The drawing is deformed so much that it will slip through the funnel, and in this case it may collapse (tear).
2. The pattern and the funnel are not deformed enough for the pattern to slip through (for this, the pattern needs to be large enough and strong enough). Then the drawing will get stuck in the funnel and block its neck for other bodies.
3. The drawing (more precisely, the material of the drawing) will destroy (tear) the material of the funnel, i.e. such a two-dimensional wormhole will be destroyed.
4. The drawing will slip past the neck of the funnel (possibly touching it with its edge). But this will only happen if you haven’t focused your design accurately enough on the direction of the neckline.

The same four options are also possible for the fall of three-dimensional physical bodies into three-dimensional wormholes. This is how illusory, using toy models as an example, I tried to describe a wormhole in the form of a tunnel without walls.

In the case of a three-dimensional wormhole (in our space), the elastic forces of the funnel material, discussed in the previous section, are replaced by gravitational tidal forces - these are the same forces that cause ebbs and flows on Earth under the influence of and.

In wormholes and black holes, tidal forces can reach monstrous levels. They are capable of tearing apart and destroying any objects or matter, and near the singularity these forces generally become infinite! However, we can assume a wormhole model in which tidal forces are limited and, thus, it is possible for our robot (or even a human) to pass through such a wormhole without harming it.

Tidal forces, according to Kip Thorne's classification, are of three types:

1. Tidal tension-compression forces
2. Tidal forces of shear deformation
3. Tidal forces of torsional deformation

Figure 3. (figure taken from the report of Kip Thorne, Nobel laureate in physics 2017) On the left is an illustration of the action of tidal tension-compression forces. On the right is an illustration of the action of tidal torsion-shear forces.

Although the last 2 types can be reduced to one - see Figure 3.

4.Einstein's general theory of relativity

In this section, I will talk about wormholes within the framework of the general theory of relativity created by Einstein. I will discuss the differences from wormholes in other theories of gravity in a subsequent section.

Why did I start my consideration with Einstein’s theory?

To date, Einstein's theory of relativity is the simplest and most beautiful of the unrefuted theories of gravity: not a single experiment to date has disproved it. The results of all experiments are in perfect agreement with it for 100 years!!! At the same time, the theory of relativity is mathematically very complex.

Why such a complex theory?

Because all other consistent theories turn out to be even more complicated...

Figure 4. (figure taken from A.D. Linde’s book “Inflationary Cosmology”)
On the left is a model of a chaotic inflationary multi-element Universe without wormholes, on the right is the same, but with wormholes.

Today, the “chaotic inflation” model is the basis of modern cosmology. This model works within the framework of Einstein’s theory and assumes the existence (besides ours) of an infinite number of other universes that arise after the “big bang”, forming during the “explosion” the so-called “space-time foam”. The first moments during and after this “explosion” are the basis of the “chaotic inflation” model.

At these moments, primary space-time tunnels (relict wormholes) may appear, which probably persist after inflation. Further, these relict wormholes connect various regions of our and other universes - see Figure 4. This model was proposed by our compatriot Andrei Linde, who is now a professor at Stanford University. This model opens up a unique opportunity to study the multi-element Universe and discover a new type of objects - entrances to wormholes.

What conditions are necessary for the existence of wormholes?

A study of wormhole models shows that exotic matter is required for their stable existence within the framework of the theory of relativity. Sometimes such matter is also called phantom matter.

Why is such matter needed?

As I wrote above, strong gravity is needed for the existence of curved space. In Einstein's theory of relativity, gravity and curved space-time exist inextricably from each other. Without enough concentrated matter, curved space straightens and the energy of this process is radiated to infinity in the form of gravitational waves.
But strong gravity alone is not enough for the stable existence of a wormhole - this way you can only get a black hole and (as a consequence) an event horizon.

In order to prevent the formation of a black hole's event horizon, phantom matter is needed. Usually, exotic or phantom matter means a violation of energy conditions by such matter. This is already a mathematical concept, but don’t be alarmed - I will describe it without mathematics. As you know from a school physics course, every physical solid body has elastic forces that resist the deformation of this body (I wrote about this in the previous section). In the more general case of arbitrary matter (liquid, gas, etc.) we speak about the intrinsic pressure of matter, or more precisely about the dependence of this pressure on the density of matter.

Physicists call this relationship the equation of state of matter.
So, in order for the energy conditions of matter to be violated, it is necessary that the sum of pressure and energy density be negative (energy density is mass density multiplied by the speed of light squared).

What does it mean?

Well, firstly, if we consider positive mass, then the pressure of such phantom matter must be negative. And secondly, the pressure of phantom matter in modulus should be large enough to give a negative value when added to the energy density.

There is an even more exotic version of phantom matter: when we immediately consider negative mass density and then pressure does not play a fundamental role, but more on that later.

And even more surprising is the fact that in the theory of relativity the density of matter (energy) depends on the frame of reference in which we consider them. For phantom matter, this leads to the fact that there is always a reference frame (moving relative to the laboratory frame almost at the speed of light) in which the density of phantom matter becomes negative. For this reason, there is no fundamental difference for phantom matter: whether its density is positive or negative.

Does such matter even exist?

And now it’s time to remember the discovery of dark energy in cosmology (do not confuse it with the concept of “dark matter” - this is a completely different substance). Dark energy was discovered in the 90s of the last century, and it was needed to explain the observed accelerated expansion of the universe. Yes, yes - the universe is not just expanding, but expanding with acceleration.

7. How wormholes could have formed in the Universe

All metric theories of gravity (and Einstein's theory among them) affirm the principle of topology conservation. This means that if a wormhole has one topology, then over time it will not be able to have another. This also means that if a space does not have the topology of a torus, then objects with the topology of a torus will not be able to appear in the same space.

Therefore, ringholes (wormholes with a torus topology) cannot appear in an expanding Universe and cannot disappear! Those. if during the “big bang” the topology was disrupted (the process of the “big bang” may not be described by a metric theory - for example, Einstein’s theory), then in the first moments of the explosion, in the “space-time foam” (I wrote about it above - ringholes, which can then turn into impassable wormholes with the same torus topology, but they will no longer be able to disappear completely - that’s why they are called relict wormholes.

But wormholes with the topology of a sphere in Einstein’s theory can appear and disappear (though in strictly topological language this will not be the same topology of a sphere as for wormholes connecting different universes, but I won’t go deeper into these mathematical jungles here) . I can again illustrate how the formation of wormholes with the topology of a sphere can occur using the example of a two-dimensional analogy - see figures No. 5 - 7 in Figure 1. Such two-dimensional wormholes can “inflate” like a child’s rubber ball at any point in a flat rubber “universe.” . Moreover, in the process of such “inflation” the topology is not violated anywhere - there are no breaks anywhere. In three-dimensional space (three-dimensional sphere), everything happens by analogy - just as I described above.

8. Is it possible to make a time machine from a wormhole?

Among literary works you can find many different novels about a time machine. Unfortunately, most of them are myths that have nothing to do with what is commonly called the TIME MACHINE in physics. So in physics, a time machine is usually called the closed world lines of material bodies. By world line we mean the trajectory of a body drawn not in space, but in space-time!

Moreover, the length of these lines must have macroscopic dimensions. The last requirement is due to the fact that in quantum physics (in the microworld) closed world lines of particles are commonplace. But the quantum world is a completely different matter. In it, for example, there is a quantum tunneling effect, which allows a microparticle to pass through a potential barrier (through an opaque wall). Remember the hero Ivanushka (played by Alexander Abdulov) in the movie Sorcerers, where he walked through the wall? A fairy tale, of course, but from a purely scientific point of view, a large macroscopic body also has the possibility of passing through a wall (quantum tunneling).

But if we calculate this probability, it turns out to be so small that the required number of attempts (which is equal to one divided by this tiny probability) required for successful quantum tunneling is almost infinity. More specifically, the number of such attempts should exceed the number of all elementary particles in the Universe!

This is roughly the same situation with the attempt to create a time machine from a quantum loop - almost unbelievable.

But we will still return to the issue of creating a time machine using a wormhole. For this (as I already said) we need closed world lines. Such lines, by the way, exist inside rotating black holes. By the way, they exist in some models of the rotating Universe (Godel’s solution).

But in order for such lines to appear inside wormholes, two conditions must be met:

Firstly, the wormhole must be a ringhole, i.e. connect different areas of the same universe.

And secondly, this wormhole must rotate quickly enough (in the right direction).

The phrase “fast enough” here means that the speed of matter moving in it should be close to the speed of light.

That's all? – you ask, will we be able to travel to the past and back? Physicists today cannot answer this question mathematically correctly. The fact is that the mathematical model that needs to be calculated is so complex that it is simply impossible to construct an analytical solution. Moreover: today there is not a single analytical solution for ringholes - there are only approximate numerical calculations made on computers.

My personal opinion is that even if it is possible to obtain a closed world line, it will be destroyed by matter (which will move along this loop) even before the loop is closed. Those. a time machine is impossible, otherwise we could go back in time and, for example, kill our grandmother there even before her children were born - an obvious contradiction in logic. Those. It is possible to obtain only time loops that cannot influence our past. For the same logical reason, we will not be able to look into the future while remaining in the present. We can only be transported entirely into the future, and it will be impossible to return from it if we have already entered it. Otherwise, the cause-and-effect relationship between events will be broken (and in my opinion this is impossible).

9. Wormholes and perpetual motion

Actually, wormholes themselves have no direct relation to perpetual motion, but with the help of phantom matter (which is necessary for the stationary existence of a wormhole), in principle, it is possible to create a so-called perpetual motion machine of the third kind.

Let me remind you of one of the amazing properties of phantom matter (see above): there is always a reference frame (moving relative to the laboratory frame almost at the speed of light) in which the density of phantom matter becomes negative. Let's imagine a body with negative mass (made of phantom matter). According to the law of universal gravitation, this body will be attracted to an ordinary body with positive mass. On the other hand, an ordinary body will have to repel from a body with negative mass. If the absolute masses of these bodies are the same, then the bodies will “chase” each other to infinity.

The principle of operation of a perpetual motion machine of the third kind is based (purely theoretically) on this effect. However, the possibility of extracting energy (for the needs of the national economy) from this principle has not been rigorously proven to date either mathematically or physically (although such attempts have been made several times).
Moreover, scientists did not and do not believe in the possibility of creating a perpetual motion machine, and this is the main argument against the existence of phantom matter and against wormholes... Personally, I also do not believe in the possibility of creating a perpetual motion machine, but I admit the possibility of the existence of certain types of phantom matter in nature.

10. The connection between wormholes and black holes

As I wrote above, the first relic wormholes that could have formed in the Universe after the “big bang” could ultimately turn out to be impassable. Those. passage through them is impossible. In mathematical terms, this means that a “trapping horizon” appears at the wormhole, sometimes also called a space-like visibility horizon. Even light cannot escape from under the trapped horizon, and even less so can other matter.

You may ask: “What, horizons are different?” Yes, there are several types of horizons in theories of gravity, and when they say that a black hole has a horizon, they usually mean an event horizon.

I will say more: a wormhole must also have a horizon, this horizon is called the visibility horizon, and there are also several types of such horizons. But I won't go into that here.

Thus, if a wormhole is impassable, then outwardly it is almost impossible to distinguish it from a black hole. The only sign of such a wormhole can only be a monopole magnetic field (although the wormhole may not have it at all).

The phrase “exclusive field” means that the field comes straight out of the wormhole in one direction, i.e. the field either comes out of the wormhole on all sides (like the needles of a hedgehog), or enters it from all sides - see Figure 6.

The existence of a monopole magnetic field in a black hole is prohibited by the so-called theorem “On the absence of hair in a black hole.”

For an electric monopole field, this property usually means that there is an electric charge inside the surface under which the field enters (or leaves). But magnetic charges have not been found in nature, so if a field enters a wormhole at one of the inputs, then it must leave it at the other entrance of the wormhole (or vice versa). Thus, it is possible to implement an interesting concept in theoretical physics, this concept is called “charge without charge”.

This means that a magnetic wormhole at each of its inputs will look like a magnetic charge, but the charges of the inputs are opposite (+ and -) and therefore the total charge of the wormhole inputs is zero. In fact, there shouldn't be any magnetic charges, it's just that the external magnetic field behaves as if there are - see Figure 6.

Passable wormholes have their own characteristic features that can be used to distinguish them from black holes, and I will write about this in the next section.
If a wormhole is impassable, then using phantom matter it can be made passable. Namely, if we “water” an impassable wormhole with phantom matter from one of its entrances, then it will become passable from the opposite entrance, and vice versa. True, the question arises and remains: how can a traveler (who wants to go through an impassable wormhole) inform his assistant at the entrance of the wormhole opposite him (closed from him by the horizon) that he (the traveler) is already near his entrance and it’s time to start “watering” ” the opposite entrance with phantom matter, so that the wormhole becomes semi-passable in the direction desired by the traveler.

Thus, in order for an impassable wormhole to become completely passable, it must be “watered” with phantom matter from both of its entrances simultaneously. Moreover, there must be a sufficient amount of phantom matter; what exactly is a difficult question; the answer to it can only be given by an accurate numerical calculation for a specific model (such models have already been calculated earlier in scientific publications). In astrophysics there was even an expression that phantom matter is so terrible that it even dissolves black holes in itself! To be fair, it should be said that a black hole, having dissolved, does not necessarily form a wormhole.

Ordinary matter in sufficient quantities, on the contrary, “locks” the wormhole, i.e. makes it impassable. Thus, we can say that in this sense, the interconversion of black holes and wormholes is possible.

11.Black and white holes as a type of wormhole

I assume that until now the reader has been under the impression that black holes are objects from which nothing can ever come out (including even light). This is not an entirely true statement.

The fact is that in almost all black holes, the singularity repels matter (and light) when it flies too close to it (already below the horizon of the black hole). The only exception to this phenomenon could be the so-called Schwarzschild black holes, i.e. those that do not rotate and have no electrical charge. But for the formation of such a Schwarzschild black hole, its constituent matter requires such initial conditions, the measure of which is zero on the set of all possible initial conditions!

In other words, when any black hole is formed, it will definitely have rotation (even if very small) and there will definitely be an electric charge (even if it’s elementary), i.e. the black hole will not be Schwarzschild. In what follows I will call such black holes real. Real black holes have their own classification: Kerr (for a rotating black hole), Reisner-Nordström (for a charged black hole) and Kerr-Newman (for a rotating and charged black hole).

What happens to a particle that is repelled by a singularity inside a real black hole?

The particle will no longer be able to fly back - this would contradict the laws of physics in a black hole, because the particle has already fallen under the event horizon. But it turns out that the topology inside black holes turns out to be non-trivial (complex). This leads to the fact that after falling under the horizon of a black hole, all matter, particles, and light are thrown out by the singularity into another universe.

In the universe where all this flies out, there is a white hole - it is from it that matter (particles, light) flies out. But all the miracles don’t end there... The fact is that in the same place in space where there is this white hole (in another universe) there is also a black hole.

Matter that falls into that black hole (in another universe) experiences a similar process and flies out into the next universe. And so on... Moreover, movement from one universe to another is always possible only in one direction: from the past to the future (in space-time). This direction is associated with the cause-and-effect relationship between events in any space-time. By virtue of common sense and logic, scientists assume that the cause-and-effect relationship should never be broken.

The reader may have a logical question: will there necessarily be a white hole in our universe - where there is already a black hole, and from where matter could fly out to us from the previous universe? For experts in the topology of black holes, this is a difficult question and the answer to it is “not always.” But, in principle, such a situation may well exist (when a black hole in our universe is also a white hole from another - previous universe). Unfortunately, we cannot yet answer the question - which situation is more probable (whether a black hole in our universe is at the same time a white hole from the previous universe or not).

So, such objects - black and white holes - also have another name: “dynamic wormholes”. They are called dynamic because they always have a region under the horizon of the black hole (this region is called the T-region) in which it is impossible to create a rigid frame of reference, and in which all particles or matter would be at rest. In the T-region, matter isn't just moving all the time—it's moving at varying speeds all the time.

But between the singularity and the T-region in real black holes there is always still a space with an ordinary region, this region is called the R-region. In particular, space outside a black hole also has the properties of an R-region. So, the repulsion of matter from the singularity occurs precisely in the internal R-region.

Figure 7. (the author took the Carter-Penrose diagram for the Reisner-Nordström black hole as the basis for the figure) The figure on the left schematically depicts a space with a non-trivial (complex) topology of the Reisner-Nordström black-and-white hole (Carter-Penrose diagram). On the right is the passage of a particle through this black-and-white hole: outside the black circle is the outer R-region, between the green and black circles is the T-region, below the green circle is the inner R-region and the singularity.

For these reasons, it is impossible to calculate and construct a single trajectory of a particle crossing a black-and-white hole in both universes at once. For such a construction, it is necessary to divide the desired trajectory into two sections and “sew” these sections together in the internal R-region (only there it is possible to do this) - see Figure 7.

As I've written before, tidal forces can tear matter apart before it reaches another universe. Moreover, inside a black-and-white hole, the maximum tidal forces are achieved at the point of minimum radius (in the inner R-region). The closer a real black hole is in its properties to a Schwarzschild one, the greater these forces will be at their maximum, and the less chance matter has to overcome the black-and-white hole without destruction.

These properties of real black holes are determined by the measure of their spin (this is their angular momentum divided by the square of their mass) and the measure of their charge (this is their charge divided by their mass). Each of these properties (these measures) cannot be greater than one for real black holes. Therefore, the greater any of these measures is to one, the less the tidal forces at their maximum will be in such a black hole, and the greater the chances for matter (or a person) to overcome such a black and white hole without destruction. Moreover, no matter how paradoxical it sounds, the heavier the real black hole is, the less tidal forces will be at its maximum!

This happens because tidal forces are not just gravitational forces, but a gradient of gravitational force (i.e., the rate of change of gravitational force). Therefore, the larger the black hole, the slower the gravitational forces change in it (despite the fact that the gravitational forces themselves can be enormous). Therefore, the gravitational gradient (i.e. tidal forces) will be smaller in larger black holes.

For example, for a black hole with a mass of several million solar masses (at the center of our galaxy there is a black hole with a mass of ≈ 4.3 million solar masses), the tidal forces on its horizon are small enough for a person to fly there and, at the same time, nothing I wouldn’t have felt it the moment it passed the horizon. And in the Universe there are also much heavier black holes - with a mass of several billion solar masses (as, for example, in the quasar M87) ... I will explain that quasars are the active (brightly glowing) nuclei of distant galaxies.

Since, as I wrote, matter or light can still fly from one universe to another through a black-and-white hole without destruction, such objects can rightfully be called another type of wormhole without phantom matter. Moreover, the existence of this particular type of dynamic wormholes in the Universe can be considered practically proven!

Original video by the author (from his publication), illustrating the free, radial fall of a dust sphere into a black and white hole (all dust particles on the sphere glow monochrome green). The Cauchy horizon radius of this black-and-white Reissner-Nordström hole is 2 times smaller than the radius of the outer horizon. The observer also falls freely and radially (following this sphere), but from a slightly greater distance.

In this case, initially green photons from dust grains of the sphere reach the observer with a red (and then violet) gravitational shift. If the observer remained motionless relative to the black-and-white hole, then after the sphere crossed the visibility horizon, the red shift of photons for the observer would become infinite and he would no longer be able to observe this dust sphere. But thanks to the free fall of the observer, he can see the sphere all the time (if we do not take into account the strong red shift of photons) - incl. and the moments when the sphere crosses both horizons, and while the observer himself crosses these horizons, and even after the sphere passes through the neck of this dynamic wormhole (black-and-white hole) - and the exit of dust particles into another universe.

Below is a radius scale for the observer (marked with a yellow mark), the point of the dust shell closest to the observer (marked with a green mark), the point of the dust shell that is furthest away from the observer from which photons come to the observer (marked with a thin white mark), as well as the location of the horizon black hole (red mark), Cauchy horizon (blue mark), and throat point (purple mark).

12.Multiverse

The concept of the Multiverse is usually identified with the non-trivial topology of the space surrounding us. Moreover, in contrast to the concept of “multiverse” in quantum physics, they mean sufficiently large spatial scales on which quantum effects can be completely neglected. What is a non-trivial topology? I will explain this with simple examples. Let's imagine two objects molded from plasticine: an ordinary cup with a handle and a saucer for this cup.

Without tearing the plasticine and without gluing the surfaces, but only by plastic deformation of the plasticine, a saucer can be turned into a ball, but it is in no way possible to turn into a cup or a donut. For a cup it’s the other way around: because of its handle, the cup cannot be turned into a saucer or into a ball, but it can be turned into a donut. These common properties of a saucer and a ball correspond to their common topology - the topology of a sphere, and the common properties of a cup and a donut - the topology of a torus.

So, the topology of a sphere (saucer and ball) is considered to be trivial, and the more complex topology of a torus (cup and donut) is considered to be non-trivial, although there are other, even more complex types of non-trivial topology - not only the topology of a torus. The Universe around us consists of at least three spatial (length, width, height) and one time dimensions, and the concepts of topology are obviously transferred to our world.

Thus, if two different universes with the topology of a sphere are connected by only one wormhole (dumbbell), then the resulting universe will also have a trivial topology of a sphere. But if two different parts of one universe are connected to each other by a wormhole (weight), then such a universe will have a non-trivial torus topology.

If two different universes with the topology of a sphere are connected by two or more wormholes, then the resulting universe will have a non-trivial topology. A system of universes connected by several wormholes will also have a nontrivial topology if there is at least one closed line that cannot be pulled together to one point by any smooth deformation.

For all their attractiveness, wormholes have two significant drawbacks: they are unstable and their existence requires the presence of exotic (or phantom) matter. And if their stability can still be realized artificially, then many scientists simply do not believe in the possibility of the existence of phantom matter. Based on the above, it may seem that without wormholes the existence of the Multiverse is impossible. But it turns out that this is not so: the existence of real black holes is quite sufficient for the existence of the Multiverse.

As I already said, inside all black holes there is a singularity - this is an area in which the density of energy and matter reaches infinite values. In almost all black holes, the singularity repels matter (and light) when it gets too close to it (already below the horizon of the black hole).

The only exception to this phenomenon could be the so-called Schwarzschild black holes, that is, those that do not rotate at all and which have no electric charge. A Schwarzschild black hole has a trivial topology. But for the formation of such a Schwarzschild black hole, the matter that forms it requires such initial conditions, the measure of which is zero on the set of all possible initial conditions!

In other words, when any black hole is formed, it will definitely have rotation (even if very small) and there will definitely be an electric charge (even if elementary), that is, the black hole will not be Schwarzschild. I call such black holes real.

A Schwarzschild black hole has a singularity inside a central sphere of infinitesimal area. A real black hole has a singularity on a ring that lies in the equatorial plane under both horizons of the black hole. It is worth adding here that, unlike the Schwarzschild black hole, a real black hole has not one, but two horizons. Moreover, between these horizons the mathematical signs of space and time change places (although this does not mean at all that space and time themselves change places, as some scientists believe).

What will happen to a particle that is repelled by a singularity inside a real black hole (already below its inner horizon)? The particle will no longer be able to fly back: this would contradict the laws of physics and causality in a black hole, since the particle has already fallen under the event horizon. This leads to the fact that after falling under the inner horizon of a real black hole, any matter, particles, light are thrown out by the singularity into another universe.

This is because, unlike Schwarzschild black holes, the topology inside real black holes turns out to be non-trivial. Isn't it amazing? Even a slight rotation of a black hole leads to a radical change in the properties of its topology! In the universe where matter then flies out, there is a white hole - everything flies out of it. But all the miracles do not end there... The fact is that in the same place in space where there is this white hole, in another universe, there is also a black hole. Matter that falls into that black hole in another universe undergoes a similar process and flies out into the next universe, and so on.

Moreover, movement from one universe to another is always possible only in one direction - from the past to the future (in space-time). This direction is associated with the cause-and-effect relationship between events in any space-time. By virtue of common sense and logic, scientists assume that the cause-and-effect relationship should never be broken. Such an object is usually called a black-and-white hole (in this sense, a wormhole could be called a white-white hole). This is the Multiverse, which exists thanks to the existence of real black holes, and the existence of wormholes and phantom matter is not necessary for its existence.

I assume that for most readers it will be difficult to imagine that in the same region of space (within the same sphere having the horizon radius of a black hole) there would be two fundamentally different objects: a black hole and a white hole. But mathematically this can be proven quite strictly.

I invite the reader to imagine a simple model: the entrance (and exit) of a building with a revolving door. This door can only rotate in one direction. Inside the building, the entrance and exit near this door are separated by turnstiles, allowing visitors to pass in only one direction (entry or exit), but outside the building there are no turnstiles. Let's imagine that inside the building these turnstiles divide the entire building into 2 parts: universe No. 1 for exiting the building and universe No. 3 for entering it, and outside the building there is universe No. 2 - the one in which you and I live. Inside the building, the turnstiles also only allow movement in the direction from No. 1 to No. 3. Such a simple model well illustrates the action of a black-and-white hole and explains that outside a building, visitors entering and exiting can collide with each other, but inside a building they cannot because of the unidirectionality of movement (just like particles of matter in the corresponding universes).

In fact, the phenomena that accompany matter during such an ejection into another universe are quite complex processes. The main role in them begins to be played by gravitational tidal forces, which I wrote about above. However, if the matter that gets inside the black hole does not reach the singularity, then the tidal forces acting on it always remain finite and, thus, it turns out to be fundamentally possible for a robot (or even a person) to pass through such a black-and-white hole without harming it. Moreover, the larger and more massive the black hole is, the smaller the tidal forces will be at their maximum...

The reader may have a logical question: will there necessarily be a white hole in our Universe where there is already a black hole, and from where matter from the previous Universe could fly out to us? For experts in black hole topology, this is a difficult question, and the answer is “not always.” But, in principle, such a situation may well exist - when a black hole in our Universe is also a white hole from another, previous universe. Answer the question “Which situation is more likely?” (whether the black hole in our Universe is also a white hole from the previous Universe or not), we, unfortunately, cannot yet.

Of course, today and in the near future it will not be technically possible to send even a robot to a black hole, but some physical effects and phenomena characteristic of wormholes and black-and-white holes have such unique properties that today observational astronomy has come close to detecting them and , as a consequence, the discovery of such objects.

13.What a wormhole should look like through a powerful telescope

As I already wrote, if a wormhole is impassable, then distinguishing it from a black hole will be very difficult. But if it is passable, then through it you can observe objects and stars in another universe.

Figure 9. (original drawing by the author)
The left panel shows a section of the starry sky observed through a circular hole in the same universe (1 million identical, evenly distributed stars). The middle panel shows the starry sky of another universe, viewed through a static wormhole (1 million different images from 210,069 identical and evenly distributed stars in another universe). The right panel shows the starry sky of another universe as seen through a black-and-white hole (1 million different images from 58,892 identical and evenly distributed stars in another universe).

Let's consider the simplest (hypothetical) model of the starry sky: there are quite a lot of identical stars in the sky, and all these stars are evenly distributed across the celestial sphere. Then the picture of this sky, observed through a circular hole in the same universe, will be as shown in the left panel of Figure 9. This left panel shows 1 million identical, evenly spaced stars, so the image appears to be an almost uniform, circular blob.

If we observe the same starry sky (in another universe) through the neck of a wormhole (from our universe), then the picture of the images of these stars will look approximately as shown in

Traveling through space and time is possible not only in science fiction films and science fiction books, a little more and it can become a reality. Many well-known and respected specialists are working on the study of such phenomena as wormholes and space-time tunnels.

A wormhole, as defined by physicist Eric Davis, is a kind of cosmic tunnel, also called a throat, connecting two distant regions in the Universe or two different Universes - if other Universes exist - or two different periods of time, or different spatial dimensions. Despite the fact that their existence has not been proven, scientists are seriously considering all possible ways to use traversable wormholes, provided they exist, to cover distances at the speed of light, and even travel through time.

Before using wormholes, scientists need to find them. Today, unfortunately, no evidence of the existence of wormholes has been discovered. But if they do exist, their location may not be as difficult as it seems at first glance.

What are wormholes?

Today, there are several theories about the origin of wormholes. Mathematician Ludwig Flamm, who used Albert Einstein's equations of relativity, was the first to coin the term “wormhole,” describing the process where gravity can bend time space related to the fabric of physical reality, resulting in the formation of a space-time tunnel.

Ali Evgun, from the Eastern Mediterranean University in Cyprus, suggests that wormholes arise in areas of dense accumulation of dark matter. According to this theory, wormholes could exist in the outer regions of the Milky Way, where there is dark matter, and within other galaxies. Mathematically, he was able to prove that there were all the necessary conditions to confirm this theory.

“In the future, it will be possible to indirectly observe similar experiments, as shown in the film Interstellar,” said Ali Evgun.

Thorne and a number of other scientists concluded that even if some wormhole were to form due to the necessary factors, it would most likely collapse before any object or person passed through it. In order to keep the wormhole open long enough, a large amount of so-called “exotic matter” would be required. One form of natural “exotic matter” is dark energy, and Davis explains its action this way: “pressure below atmospheric pressure creates a gravitational-repulsive force, which in turn pushes the interior of our Universe outward, which produces the inflationary expansion of the Universe.”

Such exotic material as dark matter is five times more abundant in the Universe than ordinary matter. Until now, scientists have not been able to detect clusters of dark matter or dark energy, so many of their properties are unknown. The study of their properties occurs through the study of the space around them.

Through a wormhole through time - reality?

The idea of ​​time travel is quite popular not only among researchers. The theory of wormholes is based on Alice's journey through the looking glass in Lewis Carroll's novel of the same name. What is a space-time tunnel? The region of space at the far end of the tunnel should stand out from the area around the entrance due to distortions similar to reflections in curved mirrors. Another sign could be the concentrated movement of light directed through the wormhole tunnel by air currents. Davis calls the phenomenon at the leading end of the wormhole the "caustic rainbow effect." Such effects can be visible from a distance. "Astronomers plan to use telescopes to hunt for these rainbow phenomena, looking for a natural or even unnaturally created, traversable wormhole," Davis said. “I’ve never heard that the project actually got off the ground.”

As part of his research into wormholes, Thorne theorized that a wormhole could be used as a time machine. Thought experiments involving time travel often run into paradoxes. Perhaps the most famous of them is the grandfather paradox: If a researcher goes back in time and kills his grandfather, then this person will not be able to be born, and therefore would never go back in time. While it may be assumed that there is no way back to time travel, Davis said Thorne's work has opened up new possibilities for scientists to explore.

Phantom Link: Wormholes and the Quantum Realm

"The entire cottage industry of theoretical physics grew out of theories that led to the development of other space-time techniques producing the described causes of time machine paradoxes," Davis said. Despite everything, the possibility of using a wormhole for time travel attracts both science fiction fans and those who want to change their past. Davis believes, based on current theories, that in order to make a time machine out of a wormhole, the flows at one or both ends of the tunnel would need to be accelerated to speeds approaching the speed of light.

"Based on this, it would be extremely difficult to build a time machine based on a wormhole," Davis said. "In comparison, it would be much easier to use wormholes for interstellar travel in space."

Other physicists have suggested that time travel through a wormhole could cause a massive build-up of energy that would destroy the tunnel before it could be used as a time machine, a process known as quantum backlash. Still, dreaming about the potential of wormholes is still fun: "Think of all the possibilities that people would have if they discovered a way to do what they could do if they could travel through time?," Davis said. "Their adventures would be very interesting, to say the least."

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Astrophysicists are sure: there are tunnels in space through which you can move to other Universes and even to other times. Presumably, they were formed when the Universe was just beginning. When, as scientists say, space “boiled” and curved.

These cosmic “time machines” were given the name “wormholes.” A “hole” differs from a black hole in that you can not only get there, but also come back. The time machine exists. And this is no longer a statement by science fiction writers - four mathematical formulas, which so far in theory prove that you can move both into the future and into the past.

And a computer model. This is roughly what a “time machine” in space should look like: two holes in space and time connected by a corridor.

“In this case we are talking about very unusual objects that were discovered in Einstein’s theory. According to this theory, in a very strong field, space is curved, and time either twists or slows down, these are fantastic properties,” explains Igor Novikov, deputy director of the Astrospace Center of the Lebedev Physical Institute.

Scientists call such unusual objects “wormholes.” This is not a human invention at all; so far only nature is capable of creating a time machine. Today, astrophysicists have only hypothetically proven the existence of “wormholes” in the Universe. It's a matter of practice.

The search for wormholes is one of the main tasks of modern astronomy. “They started talking about black holes somewhere in the late 60s, and when they made these reports, it seemed like science fiction. It seemed to everyone that this was absolute fantasy - now it’s on everyone’s lips,” says Anatoly Cherepashchuk, director of the Astronomical Institute of Moscow State University named after Sternberg. - So now “wormholes” are also science fiction, nevertheless the theory predicts that “wormholes” exist. I’m an optimist and I think that the wormholes will also be opened someday.”

“Wormholes” belong to such a mysterious phenomenon as “dark energy”, which makes up 70 percent of the Universe. “Dark energy has now been discovered - it is a vacuum that has negative pressure. And in principle, “wormholes” could be formed from a state of vacuum,” suggests Anatoly Cherepashchuk. One of the habitats of “wormholes” is the centers of galaxies. But the main thing here is not to confuse them with black holes, huge objects that are also located at the center of galaxies.

Their mass is billions of our Suns. At the same time, black holes have a powerful gravitational force. It is so large that even light cannot escape from there, so it is impossible to see them with a regular telescope. The gravitational force of wormholes is also enormous, but if you look inside the wormhole, you can see the light of the past.

“In the center of galaxies, in their cores, there are very compact objects, these are black holes, but it is assumed that some of these black holes are not black holes at all, but entrances to these “wormholes,” says Igor Novikov. Today, more than three hundred black holes have been discovered.

From Earth to the center of our Milky Way galaxy is 25 thousand light years. If it turns out that this black hole is a “wormhole”, a corridor for time travel, humanity will have to fly and fly to it.