BLACK HOLE
a region in space resulting from the complete gravitational collapse of matter, in which the gravitational attraction is so strong that neither matter, nor light, nor other information carriers can leave it. Therefore, the interior of a black hole is not causally connected to the rest of the universe; Physical processes occurring inside a black hole cannot influence processes outside it. A black hole is surrounded by a surface with the property of a unidirectional membrane: matter and radiation freely fall through it into the black hole, but nothing can escape from there. This surface is called the "event horizon". Since there are still only indirect indications of the existence of black holes at distances of thousands of light years from the Earth, our further presentation is based mainly on theoretical results. Black holes, predicted by the general theory of relativity (the theory of gravity proposed by Einstein in 1915) and other, more modern theories of gravity, were mathematically substantiated by R. Oppenheimer and H. Snyder in 1939. But the properties of space and time in the vicinity of these objects turned out to be so unusual, that astronomers and physicists did not take them seriously for 25 years. However, astronomical discoveries in the mid-1960s brought black holes to the surface as a possible physical reality. Their discovery and study can fundamentally change our ideas about space and time.
Formation of black holes. While thermonuclear reactions occur in the bowels of the star, they maintain high temperature and pressure, preventing the star from collapsing under the influence of its own gravity. However, over time, the nuclear fuel is depleted, and the star begins to shrink. Calculations show that if the mass of a star does not exceed three solar masses, then it will win the “battle with gravity”: its gravitational collapse will be stopped by the pressure of “degenerate” matter, and the star will forever turn into a white dwarf or neutron star. But if the mass of the star is more than three solar, then nothing can stop its catastrophic collapse and it will quickly go under the event horizon, becoming a black hole. For a spherical black hole of mass M, the event horizon forms a sphere with a circle at the equator 2p times larger than the “gravitational radius” of the black hole RG = 2GM/c2, where c is the speed of light and G is the gravitational constant. A black hole with a mass of 3 solar masses has a gravitational radius of 8.8 km.

If an astronomer observes a star at the moment of its transformation into a black hole, then at first he will see how the star is compressing faster and faster, but as its surface approaches the gravitational radius, the compression will begin to slow down until it stops completely. At the same time, the light coming from the star will weaken and redden until it goes out completely. This happens because, in the fight against the gigantic force of gravity, the light loses energy and it takes more and more time for it to reach the observer. When the star's surface reaches the gravitational radius, the light that leaves it will take an infinite amount of time to reach the observer (and the photons will lose all their energy). Consequently, the astronomer will never wait for this moment, much less see what is happening to the star below the event horizon. But theoretically this process can be studied. Calculations of idealized spherical collapse show that in a short time the star collapses to a point where infinitely high values ​​of density and gravity are achieved. Such a point is called "singularity". Moreover, general mathematical analysis shows that if an event horizon has arisen, then even a non-spherical collapse leads to a singularity. However, all this is true only if general relativity applies down to very small spatial scales, which we are not yet sure of. Quantum laws operate in the microworld, but the quantum theory of gravity has not yet been created. It is clear that quantum effects cannot stop the collapse of a star into a black hole, but they could prevent the appearance of a singularity. The modern theory of stellar evolution and our knowledge of the stellar population of the Galaxy indicate that among its 100 billion stars there should be about 100 million black holes formed during the collapse of the most massive stars. In addition, black holes of very large masses can be located in the cores of large galaxies, including ours. As already noted, in our era, only a mass more than three times the solar mass can become a black hole. However, immediately after the Big Bang, from which approx. 15 billion years ago, the expansion of the Universe began, black holes of any mass could be born. The smallest of them, due to quantum effects, should have evaporated, losing their mass in the form of radiation and particle flows. But “primary black holes” with a mass of more than 1015 g could survive to this day. All calculations of stellar collapse are made under the assumption of a slight deviation from spherical symmetry and show that an event horizon is always formed. However, with a strong deviation from spherical symmetry, the collapse of a star can lead to the formation of a region with infinitely strong gravity, but not surrounded by an event horizon; it is called the "naked singularity". This is no longer a black hole in the sense we discussed above. Physical laws near a naked singularity can take a very unexpected form. Currently, a naked singularity is considered an unlikely object, while most astrophysicists believe in the existence of black holes.
Properties of black holes. To an outside observer, the structure of a black hole looks extremely simple. During the collapse of a star into a black hole in a small fraction of a second (according to a remote observer's clock), all its external features associated with the inhomogeneity of the original star are emitted in the form of gravitational and electromagnetic waves. The resulting stationary black hole “forgets” all information about the original star, except for three quantities: total mass, angular momentum (associated with rotation) and electric charge. By studying a black hole, it is no longer possible to know whether the original star consisted of matter or antimatter, whether it had the shape of a cigar or a pancake, etc. Under real astrophysical conditions, a charged black hole will attract particles of the opposite sign from the interstellar medium, and its charge will quickly become zero. The remaining stationary object will either be a non-rotating "Schwarzschild black hole", which is characterized only by mass, or a rotating "Kerr black hole", which is characterized by mass and angular momentum. The uniqueness of the above types of stationary black holes was proven within the framework of the general theory of relativity by W. Israel, B. Carter, S. Hawking and D. Robinson. According to the general theory of relativity, space and time are curved by the gravitational field of massive bodies, with the greatest curvature occurring near black holes. When physicists talk about intervals of time and space, they mean numbers read from some physical clock or ruler. For example, the role of a clock can be played by a molecule with a certain vibration frequency, the number of which between two events can be called a “time interval.” It is remarkable that gravity affects all physical systems in the same way: all clocks show that time is slowing down, and all rulers show that space is stretching near a black hole. This means that the black hole bends the geometry of space and time around itself. Far from the black hole, this curvature is small, but close to it it is so large that light rays can move around it in a circle. Far from a black hole, its gravitational field is exactly described by Newton's theory for a body of the same mass, but close to it, gravity becomes much stronger than Newton's theory predicts. Any body falling into a black hole will be torn apart long before crossing the event horizon by powerful tidal gravitational forces arising from differences in gravity at different distances from the center. A black hole is always ready to absorb matter or radiation, thereby increasing its mass. Its interaction with the outside world is determined by a simple Hawking principle: the area of ​​the event horizon of a black hole never decreases, unless one takes into account the quantum production of particles. J. Bekenstein in 1973 suggested that black holes obey the same physical laws as physical bodies that emit and absorb radiation (the “absolutely black body” model). Influenced by this idea, Hawking showed in 1974 that black holes can emit matter and radiation, but this will only be noticeable if the mass of the black hole itself is relatively small. Such black holes could be born immediately after the Big Bang, which began the expansion of the Universe. The masses of these primary black holes should be no more than 1015 g (like a small asteroid), and their size should be 10-15 m (like a proton or neutron). The powerful gravitational field near a black hole produces particle-antiparticle pairs; one of the particles of each pair is absorbed by the hole, and the second is emitted outward. A black hole with a mass of 1015 g should behave like a body with a temperature of 1011 K. The idea of ​​\u200b\u200b“evaporation” of black holes completely contradicts the classical concept of them as bodies that are not capable of radiating.
Search for black holes. Calculations within the framework of Einstein's general theory of relativity only indicate the possibility of the existence of black holes, but do not at all prove their presence in the real world; the discovery of a real black hole would be an important step in the development of physics. Finding isolated black holes in space is hopelessly difficult: we will not be able to notice a small dark object against the background of cosmic blackness. But there is hope to detect a black hole by its interaction with surrounding astronomical bodies, by its characteristic influence on them. Supermassive black holes can reside in the centers of galaxies, continuously devouring stars there. Concentrated around the black hole, the stars should form central brightness peaks in the galactic nuclei; Their search is now actively underway. Another search method is to measure the speed of stars and gas around a central object in the galaxy. If their distance from the central object is known, then its mass and average density can be calculated. If it significantly exceeds the density possible for star clusters, then it is believed that it is a black hole. Using this method, in 1996 J. Moran and his colleagues determined that in the center of the galaxy NGC 4258 there is probably a black hole with a mass of 40 million solar. The most promising is to search for a black hole in binary systems, where it, paired with a normal star, can orbit around a common center of mass. By the periodic Doppler shift of lines in the spectrum of a star, one can understand that it is orbiting in tandem with a certain body and even estimate the mass of the latter. If this mass exceeds 3 solar masses, and the radiation of the body itself cannot be detected, then it is very possible that it is a black hole. In a compact binary system, the black hole can capture gas from the surface of a normal star. Moving in orbit around the black hole, this gas forms a disk and, as it spirals toward the black hole, it becomes very hot and becomes a source of powerful X-ray radiation. Rapid fluctuations in this radiation should indicate that the gas is rapidly moving in a small radius orbit around a tiny, massive object. Since the 1970s, several X-ray sources have been discovered in binary systems with clear signs of black holes. The most promising is the X-ray binary V 404 Cygni, the mass of the invisible component of which is estimated to be no less than 6 solar masses. Other remarkable black hole candidates are in the X-ray binaries Cygnus X-1, LMCX-3, V 616 Monoceros, QZ Vulpeculae, and the X-ray novae Ophiuchus 1977, Mukha 1981, and Scorpius 1994. With the exception of LMCX-3, located in the Large Magellanic Cloud, all of them are located in our Galaxy at distances of about 8000 light years. years from Earth.
see also
COSMOLOGY;
GRAVITY;
GRAVITATIONAL COLLAPSE;
RELATIVITY;
EXTRA-ATMOSPHERE ASTRONOMY.
LITERATURE
Cherepashchuk A.M. Masses of black holes in binary systems. Advances in Physical Sciences, vol. 166, p. 809, 1996

Collier's Encyclopedia. - Open Society. 2000 .

Synonyms:

See what a “BLACK HOLE” is in other dictionaries:

BLACK HOLE, a localized area of ​​outer space from which neither matter nor radiation can escape, in other words, the first cosmic speed exceeds the speed of light. The boundary of this area is called the event horizon.... ... Scientific and technical encyclopedic dictionary

Cosmic an object that arises as a result of the compression of a body by gravity. forces to sizes smaller than its gravitational radius rg=2g/c2 (where M is the mass of the body, G is the gravitational constant, c is the numerical value of the speed of light). Prediction about the existence of... ... Physical encyclopedia

Noun, number of synonyms: 2 star (503) unknown (11) ASIS Dictionary of Synonyms. V.N. Trishin. 2013… Synonym dictionary

Every person who gets acquainted with astronomy sooner or later experiences a strong curiosity about the most mysterious objects of the Universe - black holes. These are real lords of darkness, capable of “swallowing” any atom passing nearby and not allowing even light to escape - their attraction is so powerful. These objects pose a real challenge for physicists and astronomers. The former cannot yet understand what happens to the matter that falls inside the black hole, and the latter, although they explain the most energy-consuming phenomena in space by the existence of black holes, have never had the opportunity to observe any of them directly. We will tell you about these interesting celestial objects, find out what has already been discovered and what remains to be learned in order to lift the veil of secrecy.

What is a black hole?

The name “black hole” (in English - black hole) was proposed in 1967 by the American theoretical physicist John Archibald Wheeler (see photo on the left). It served to designate a celestial body, the attraction of which is so strong that even light does not let go of itself. That is why it is “black” because it does not emit light.

Indirect observations

This is the reason for such mystery: since black holes do not glow, we cannot see them directly and are forced to look for and study them using only indirect evidence that their existence leaves in the surrounding space. In other words, if a black hole engulfs a star, we cannot see the black hole, but we can observe the devastating effects of its powerful gravitational field.

Laplace's intuition

Although the expression “black hole” to denote the hypothetical final stage of the evolution of a star that has collapsed into itself under the influence of gravity is relatively recent, the idea of ​​the possibility of the existence of such bodies arose more than two centuries ago. The Englishman John Michell and the Frenchman Pierre-Simon de Laplace independently hypothesized the existence of “invisible stars”; at the same time, they were based on the usual laws of dynamics and Newton’s law of universal gravitation. Today, black holes have received their correct description based on Einstein's general theory of relativity.

In his work “Exposition of the System of the World” (1796), Laplace wrote: “A bright star of the same density as the Earth, with a diameter 250 times greater than the diameter of the Sun, would, thanks to its gravitational attraction, prevent light rays from reaching us. Therefore, it is possible that the largest and brightest celestial bodies are invisible for this reason.”

Invincible gravity

Laplace's idea was based on the concept of escape velocity (second cosmic velocity). A black hole is such a dense object that its gravity can hold back even light, which develops the highest speed in nature (almost 300,000 km/s). In practice, escaping from a black hole requires speeds greater than the speed of light, but this is impossible!

This means that a star of this kind will be invisible, since even light will not be able to overcome its powerful gravity. Einstein explained this fact through the phenomenon of light bending under the influence of a gravitational field. In reality, near a black hole, space-time is so curved that the trajectories of light rays also close on themselves. In order to turn the Sun into a black hole, we will have to concentrate all of its mass in a ball with a radius of 3 km, and the Earth will have to turn into a ball with a radius of 9 mm!

Types of black holes

Just about ten years ago, observations suggested the existence of two types of black holes: stellar, whose mass is comparable to the mass of the Sun or slightly exceeds it, and supermassive, whose mass ranges from several hundred thousand to many millions of solar masses. However, relatively recently, X-ray images and high-resolution spectra obtained from artificial satellites such as Chandra and XMM-Newton brought to the fore a third type of black hole - with an average mass exceeding the mass of the Sun by thousands of times.

Stellar black holes

Stellar black holes became known earlier than others. They are formed when a large-mass star, at the end of its evolutionary path, exhausts its reserves of nuclear fuel and collapses into itself due to its own gravity. An explosion that shakes a star (a phenomenon known as a “supernova explosion”) has catastrophic consequences: if the star’s core is more than 10 times the mass of the Sun, no nuclear force can resist the gravitational collapse that will result in the creation of a black hole.

Supermassive black holes

Supermassive black holes, first noted in the nuclei of some active galaxies, have a different origin. There are several hypotheses regarding their birth: a stellar black hole, which over the course of millions of years devours all the stars around it; a cluster of black holes merging together; a colossal gas cloud collapsing directly into a black hole. These black holes are among the most energetic objects in space. They are located at the centers of many, if not all, galaxies. Our Galaxy also has such a black hole. Sometimes, due to the presence of such a black hole, the cores of these galaxies become very bright. Galaxies with black holes at the center, surrounded by large amounts of falling matter and therefore capable of producing colossal amounts of energy, are called "active" and their cores are called "active galactic nuclei" (AGN). For example, quasars (the most distant cosmic objects from us that are accessible to our observation) are active galaxies in which we see only a very bright core.

Medium and mini

Another mystery remains the medium-mass black holes, which, according to recent research, may be at the center of some globular clusters, such as M13 and NCC 6388. Many astronomers are skeptical about these objects, but some new research suggests the presence of black holes medium-sized even near the center of our Galaxy. English physicist Stephen Hawking also put forward a theoretical assumption about the existence of a fourth type of black hole - a “mini-hole” with a mass of only a billion tons (which is approximately equal to the mass of a large mountain). We are talking about primary objects, that is, those that appeared in the first moments of the life of the Universe, when the pressure was still very high. However, not a single trace of their existence has yet been discovered.

How to find a black hole

Just a few years ago, a light came on over black holes. Thanks to constantly improving instruments and technologies (both ground-based and space-based), these objects are becoming less and less mysterious; more precisely, the space surrounding them becomes less mysterious. In fact, since the black hole itself is invisible, we can only recognize it if it is surrounded by enough matter (stars and hot gas) orbiting around it at a short distance.

Watching binary systems

Some stellar black holes have been discovered by observing the orbital motion of a star around an unseen companion in a binary system. Close binary systems (that is, consisting of two stars very close to each other), in which one of the companions is invisible, are a favorite object of observation for astrophysicists searching for black holes.

An indication of the presence of a black hole (or neutron star) is the strong emission of X-rays caused by a complex mechanism that can be schematically described as follows. Thanks to its powerful gravity, a black hole can rip matter out of its companion star; this gas spreads out into a flat disk and spirals down into the black hole. Friction resulting from collisions between particles of falling gas heats the inner layers of the disk to several million degrees, which causes powerful X-ray radiation.

X-ray observations

X-ray observations of objects in our Galaxy and neighboring galaxies, carried out for several decades, have made it possible to detect compact binary sources, about a dozen of which are systems containing black hole candidates. The main problem is determining the mass of an invisible celestial body. The mass (although not very precise) can be found by studying the motion of the companion or, much more difficult, by measuring the intensity of the X-ray radiation of the falling material. This intensity is related by an equation to the mass of the body on which this substance falls.

Nobel laureate

Something similar can be said for supermassive black holes observed in the cores of many galaxies, the masses of which are estimated by measuring the orbital velocities of the gas falling into the black hole. In this case, caused by the powerful gravitational field of a very large object, a rapid increase in the speed of gas clouds orbiting in the center of galaxies is detected by observations in the radio range, as well as in optical rays. Observations in the X-ray range can confirm the increased release of energy caused by matter falling into the black hole. Research in X-rays was started in the early 1960s by the Italian Riccardo Giacconi, who worked in the USA. His Nobel Prize in 2002 recognized his "pioneering contributions to astrophysics leading to the discovery of X-ray sources in space."

Cygnus X-1: first candidate

Our Galaxy is not immune to the presence of candidate black hole objects. Fortunately, none of these objects are close enough to us to pose a threat to the existence of Earth or the solar system. Despite the large number of compact X-ray sources that have been identified (and these are the most likely candidates for black holes), we have no confidence that they actually contain black holes. The only one among these sources that does not have an alternative version is the close binary system Cygnus X-1, that is, the brightest source of X-ray radiation in the constellation Cygnus.

Massive stars

This system, whose orbital period is 5.6 days, consists of a very bright blue star of large size (its diameter is 20 times that of the Sun, and its mass is about 30 times larger), easily visible even in your telescope, and an invisible second star, the mass of which is estimated at several solar masses (up to 10). Located 6,500 light-years away, the second star would be perfectly visible if it were an ordinary star. Its invisibility, the powerful X-ray emission produced by the system and, finally, the mass estimate lead most astronomers to believe that this is the first confirmed discovery of a stellar black hole.

Doubts

However, there are also skeptics. Among them is one of the largest researchers of black holes, physicist Stephen Hawking. He even made a bet with his American colleague Keel Thorne, an ardent supporter of classifying the Cygnus X-1 object as a black hole.

The debate over the identity of the Cygnus X-1 object is not Hawking's only bet. Having devoted several nine years to theoretical studies of black holes, he became convinced of the fallacy of his previous ideas about these mysterious objects. In particular, Hawking assumed that matter, after falling into a black hole, disappears forever, and with it all of its information luggage disappears. He was so sure of this that he made a bet on this topic in 1997 with his American colleague John Preskill.

Admitting a mistake

On July 21, 2004, in his speech at the Congress on the Theory of Relativity in Dublin, Hawking admitted that Preskill was right. Black holes do not lead to the complete disappearance of matter. Moreover, they have a certain kind of “memory”. They may well contain traces of what they have consumed. Thus, by “evaporating” (that is, slowly emitting radiation due to the quantum effect), they can return this information to our Universe.

Black holes in the Galaxy

Astronomers still have many doubts about the presence of stellar black holes (like the one belonging to the binary system Cygnus X-1) in our Galaxy; but there is much less doubt about supermassive black holes.

In the center

Our Galaxy has at least one supermassive black hole. Its source, known as Sagittarius A*, is precisely localized in the center of the plane of the Milky Way. Its name is explained by the fact that it is the most powerful radio source in the constellation Sagittarius. It is in this direction that both the geometric and physical centers of our galactic system are located. Located about 26,000 light-years away, the supermassive black hole associated with radio wave source Sagittarius A* has a mass estimated at about 4 million solar masses, contained in a space the volume of which is comparable to the volume of the solar system. Its relative proximity to us (it is by far the closest supermassive black hole to Earth) has led to the object being studied particularly closely in recent years by the Chandra space observatory. It turned out, in particular, that it is also a powerful source of X-ray radiation (but not as powerful as sources in active galactic nuclei). Sagittarius A* may be a dormant remnant of what was the active core of our Galaxy millions or billions of years ago.

Second black hole?

However, some astronomers believe that there is another surprise in our Galaxy. We are talking about a second black hole of average mass, holding together a cluster of young stars and preventing them from falling into a supermassive black hole located in the center of the Galaxy itself. How can it be that at a distance of less than one light year from it there could be a star cluster that is barely 10 million years old, that is, by astronomical standards, very young? According to the researchers, the answer is that the cluster was not born there (the environment around the central black hole is too hostile for star formation), but was “pulled” there due to the existence of a second black hole inside it, which has an average mass.

In orbit

Individual stars in the cluster, attracted by the supermassive black hole, began to shift towards the galactic center. However, instead of scattering into space, they remain gathered together thanks to the gravitational pull of a second black hole located at the center of the cluster. The mass of this black hole can be estimated based on its ability to hold an entire star cluster on a leash. A medium-sized black hole apparently takes about 100 years to orbit the central black hole. This means that long-term observations over many years will allow us to “see” it.

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Consider the mysterious and invisible black holes in the Universe: interesting facts, Einstein's research, supermassive and intermediate types, theory, structure.

- one of the most interesting and mysterious objects in outer space. They have a high density, and the gravitational force is so powerful that even light cannot escape beyond its limits.

Albert Einstein first spoke about black holes in 1916, when he created the general theory of relativity. The term itself originated in 1967 thanks to John Wheeler. And the first black hole was “seen” in 1971.

The classification of black holes includes three types: stellar mass black holes, supermassive black holes and intermediate mass black holes. Be sure to watch the video about black holes to learn many interesting facts and get to know these mysterious cosmic formations better.

Interesting facts about black holes

• If you find yourself inside a black hole, gravity will stretch you. But there is no need to be afraid, because you will die before you reach the singularity. A 2012 study suggested that quantum effects turn the event horizon into a wall of fire that turns you into a pile of ash.
• Black holes don't "suck". This process is caused by a vacuum, which is not present in this formation. So the material just falls off.
• The first black hole was Cygnus X-1, found by rockets with Geiger counters. In 1971, scientists received a radio signal from Cygnus X-1. This object became the subject of a dispute between Kip Thorne and Stephen Hawking. The latter believed that it was not a black hole. In 1990, he admitted defeat.
• Tiny black holes may have appeared immediately after the Big Bang. Rapidly rotating space compressed some areas into dense holes, less massive than the Sun.
• If the star gets too close, it could be torn apart.
• It is generally estimated that there are up to a billion stellar black holes with three times the mass of the Sun.
• If we compare string theory and classical mechanics, the former gives rise to more varieties of massive giants.

The danger of black holes

When a star runs out of fuel, it can begin the process of self-destruction. If its mass was three times that of the Sun, then the remaining core would become a neutron star or a white dwarf. But the larger star transforms into a black hole.

Such objects are small, but have incredible density. Imagine that in front of you is an object the size of a city, but its mass is three times that of the Sun. This creates an incredibly huge gravitational force that attracts dust and gas, increasing its size. You will be surprised, but there may be several hundred million stellar black holes.

Supermassive black holes

Of course, nothing in the universe compares to the awesomeness of supermassive black holes. They exceed the solar mass by billions of times. It is believed that such objects exist in almost every galaxy. Scientists do not yet know all the intricacies of the formation process. Most likely, they grow due to the accumulation of mass from surrounding dust and gas.

They may owe their scale to the merger of thousands of small black holes. Or an entire star cluster could collapse.

Black holes at the centers of galaxies

Astrophysicist Olga Silchenko about the discovery of a supermassive black hole in the Andromeda nebula, John Kormendy's research and dark gravitating bodies:

The nature of cosmic radio sources

Astrophysicist Anatoly Zasov about synchrotron radiation, black holes in the nuclei of distant galaxies and neutral gas:

Intermediate black holes

Not long ago, scientists found a new type - intermediate mass black holes. They can form when stars in a cluster collide, causing a chain reaction. As a result, they fall into the center and form a supermassive black hole.

In 2014, astronomers discovered an intermediate type in the arm of a spiral galaxy. They are very difficult to find because they can be located in unpredictable places.

Micro black holes

Physicist Eduard Boos on the safety of the LHC, the birth of a microblack hole and the concept of a membrane:

Black hole theory

Black holes are extremely massive objects, but span a relatively modest amount of space. In addition, they have enormous gravity, preventing objects (and even light) from leaving their territory. However, it is impossible to see them directly. Researchers have to look at the radiation produced when a black hole feeds.

Interestingly, it happens that matter heading towards a black hole bounces off the event horizon and is thrown out. In this case, bright jets of material are formed, moving at relativistic speeds. These emissions can be detected over long distances.

- amazing objects in which the force of gravity is so enormous that it can bend light, warp space and distort time.

In black holes, three layers can be distinguished: the outer and inner event horizon and the singularity.

The event horizon of a black hole is the boundary where light has no chance of escaping. Once a particle crosses this line, it will not be able to leave. The inner region where the mass of a black hole is located is called a singularity.

If we speak from the position of classical mechanics, then nothing can escape a black hole. But quantum makes its own correction. The fact is that every particle has an antiparticle. They have the same masses, but different charges. If they intersect, they can annihilate each other.

When such a pair appears outside the event horizon, one of them can be pulled in and the other can be repelled. Because of this, the horizon can shrink and the black hole can collapse. Scientists are still trying to study this mechanism.

Accretion

Astrophysicist Sergei Popov on supermassive black holes, planet formation and accretion of matter in the early Universe:

The most famous black holes

Frequently asked questions about black holes

More capaciously, a black hole is a certain area in space in which such a huge amount of mass is concentrated that not a single object can escape the gravitational influence. When it comes to gravity, we rely on the general theory of relativity proposed by Albert Einstein. To understand the details of the object under study, we will move step by step.

Let's imagine that you are on the surface of the planet and are throwing a boulder. If you don't have the power of the Hulk, you won't be able to exert enough force. Then the stone will rise to a certain height, but under the pressure of gravity it will fall back. If you have the hidden potential of a green strongman, then you are able to give the object sufficient acceleration, thanks to which it will completely leave the zone of gravitational influence. This is called "escape velocity".

If we break it down into a formula, this speed depends on the planetary mass. The larger it is, the more powerful the gravitational grip. The speed of departure will depend on where exactly you are: the closer to the center, the easier it is to get out. The speed of departure of our planet is 11.2 km/s, but it is 2.4 km/s.

We are getting closer to the most interesting part. Let's say you have an object with an incredible concentration of mass collected in a tiny place. In this case, the escape velocity exceeds the speed of light. And we know that nothing moves faster than this indicator, which means that no one will be able to overcome such force and escape. Even a light beam cannot do this!

Back in the 18th century, Laplace pondered the extreme concentration of mass. Following general relativity, Karl Schwarzschild was able to find a mathematical solution to the theory's equation to describe such an object. Further contributions were made by Oppenheimer, Wolkoff and Snyder (1930s). From that moment on, people began to discuss this topic seriously. It became clear: when a massive star runs out of fuel, it is unable to withstand the force of gravity and is bound to collapse into a black hole.

In Einstein's theory, gravity is a manifestation of curvature in space and time. The fact is that the usual geometric rules do not work here and massive objects distort space-time. The black hole has bizarre properties, so its distortion is most clearly visible. For example, an object has an “event horizon.” This is the surface of the sphere marking the line of the hole. That is, if you step over this limit, then there is no turning back.

Literally, this is the place where the escape speed is equal to the speed of light. Outside this place, the escape velocity is inferior to the speed of light. But if your rocket is able to accelerate, then there will be enough energy to escape.

The horizon itself is quite strange in terms of geometry. If you are far away, you will feel like you are looking at a static surface. But if you get closer, you realize that it is moving outward at the speed of light! Now I understand why it is easy to enter, but so difficult to escape. Yes, this is very confusing, because in fact the horizon stands still, but at the same time it rushes at the speed of light. It's like the situation with Alice, who had to run as fast as possible just to stay in place.

When hitting the horizon, space and time experience such a strong distortion that the coordinates begin to describe the roles of radial distance and switching time. That is, “r”, marking the distance from the center, becomes temporary, and “t” is now responsible for “spatiality”. As a result, you will not be able to stop moving with a lower index of r, just as you will not be able to get into the future in normal time. You will come to a singularity where r = 0. You can throw rockets, run the engine to maximum, but you cannot escape.

The term "black hole" was coined by John Archibald Wheeler. Before that, they were called “cooled stars.”

Physicist Emil Akhmedov on the study of black holes, Karl Schwarzschild and giant black holes:

There are two ways to calculate how big something is. You can name the mass or how large the area occupies. If we take the first criterion, then there is no specific limit on the massiveness of a black hole. You can use any amount as long as you can compress it to the required density.

Most of these formations appeared after the death of massive stars, so one would expect that their weight should be equivalent. The typical mass for such a hole would be 10 times that of the sun - 10 31 kg. In addition, each galaxy must be home to a central supermassive black hole, whose mass exceeds the solar one a million times - 10 36 kg.

The more massive the object, the more mass it covers. The horizon radius and mass are directly proportional, that is, if a black hole weighs 10 times more than another, then its radius is 10 times larger. The radius of a hole with solar massiveness is 3 km, and if it is a million times larger, then 3 million km. These seem to be incredibly massive things. But let's not forget that these are standard concepts for astronomy. The solar radius reaches 700,000 km, and that of a black hole is 4 times greater.

Let's say that you are unlucky and your ship is inexorably moving towards a supermassive black hole. There's no point in fighting. You simply turn off the engines and head towards the inevitable. What to expect?

Let's start with weightlessness. You are in free fall, so the crew, ship and all the parts are weightless. The closer you get to the center of the hole, the stronger the tidal gravitational forces are felt. For example, your feet are closer to the center than your head. Then you begin to feel like you are being stretched. As a result, you will simply be torn apart.

These forces are unnoticeable until you get within 600,000 km of the center. This is already after the horizon. But we are talking about a huge object. If you fall into a hole with the mass of the sun, then the tidal forces would engulf you 6000 km from the center and tear you apart before you reach the horizon (that's why we send you to the big one so that you can die already inside the hole, and not on the approach) .

What is inside? I don't want to disappoint, but nothing remarkable. Some objects may be distorted in appearance and nothing else out of the ordinary. Even after crossing the horizon, you will see things around you as they move with you.

How long will all this take? Everything depends on your distance. For example, you started from a point of rest where the singularity is 10 times the radius of the hole. It will take only 8 minutes to approach the horizon, and then another 7 seconds to enter the singularity. If you fall into a small black hole, everything will happen faster.

As soon as you cross the horizon, you can shoot rockets, scream and cry. You have 7 seconds to do all this until you get into the singularity. But nothing will save you. So just enjoy the ride.

Let's say you are doomed and fall into a hole, and your boyfriend watches from afar. Well, he'll see things differently. You will notice that you slow down as you get closer to the horizon. But even if a person sits for a hundred years, he will not wait until you reach the horizon.

Let's try to explain. The black hole could have emerged from a collapsing star. Since the material is destroyed, Kirill (let him be your friend) sees it decreasing, but will never notice it approaching the horizon. That's why they were called "frozen stars" because they seem to freeze at a certain radius.

What's the matter? Let's call it an optical illusion. Infinity is not needed to form a hole, just as it is not necessary to cross the horizon. As you approach, the light takes longer to reach Kirill. More precisely, the real-time radiation from your transition will be recorded at the horizon forever. You have long stepped over the line, and Kirill is still observing the light signal.

Or you can approach from the other side. Time drags longer near the horizon. For example, you have a super-powerful ship. You managed to get closer to the horizon, stay there for a couple of minutes and get out alive to Kirill. Who will you see? Old man! After all, time passed much slower for you.

What is true then? Illusion or game of time? It all depends on the coordinate system used to describe the black hole. If you rely on Schwarzschild coordinates, then when crossing the horizon, the time coordinate (t) is equated to infinity. But the system's metrics provide a blurred view of what's happening near the object itself. At the horizon line, all coordinates are distorted (singularity). But you can use both coordinate systems, so the two answers are valid.

In reality, you will simply become invisible, and Kirill will stop seeing you before much time has passed. Don't forget about redshift. You emit observable light at a certain wavelength, but Kirill will see it at a longer one. The waves lengthen as they approach the horizon. In addition, do not forget that radiation occurs in certain photons.

For example, at the moment of transition you will send the last photon. It will reach Kirill at a certain finite time (about an hour for a supermassive black hole).

Of course not. Don't forget about the existence of the event horizon. This is the only area you can't get out of. It is enough just not to approach her and feel calm. Moreover, from a safe distance this object will seem very ordinary to you.

Hawking's information paradox

Physicist Emil Akhmedov on the effect of gravity on electromagnetic waves, the information paradox of black holes and the principle of predictability in science:

Don't panic, as the Sun will never transform into such an object because it simply doesn't have enough mass. Moreover, it will retain its current appearance for another 5 billion years. Then it will move to the red giant stage, absorbing Mercury, Venus and thoroughly frying our planet, and then become an ordinary white dwarf.

But let's indulge in fantasy. So the Sun became a black hole. To begin with, we will immediately be enveloped in darkness and cold. The Earth and other planets will not be sucked into the hole. They will continue to orbit the new object in normal orbits. Why? Because the horizon will reach only 3 km, and gravity will not be able to do anything to us.

Yes. Naturally, we cannot rely on visible observation, since the light cannot escape. But there is circumstantial evidence. For example, you see an area that could contain a black hole. How can I check this? Start by measuring the mass. If it is clear that in one area there is too much of it or it is seemingly invisible, then you are on the right track. There are two search points: the galactic center and binary systems with X-ray radiation.

Thus, massive central objects were found in 8 galaxies, whose nuclear mass ranges from a million to a billion solar. Mass is calculated by observing the speed of rotation of stars and gas around the center. The faster, the greater the mass must be to keep them in orbit.

These massive objects are considered black holes for two reasons. Well, there are simply no more options. There is nothing more massive, darker and more compact. In addition, there is a theory that all active and large galaxies have such a monster hiding in the center. But still this is not 100% proof.

But two recent findings speak in favor of the theory. A “water maser” system (a powerful source of microwave radiation) near the nucleus was noticed in the nearest active galaxy. Using an interferometer, scientists mapped the distribution of gas velocities. That is, they measured the speed within half a light year at the galactic center. This helped them understand that there was a massive object inside, whose radius reached half a light year.

The second find is even more convincing. Researchers using X-rays stumbled upon a spectral line of the galactic core, indicating the presence of atoms nearby, the speed of which is incredibly high (1/3 the speed of light). In addition, the emission corresponded to a redshift that corresponds to the horizon of the black hole.

Another class can be found in the Milky Way. These are stellar black holes that form after a supernova explosion. If they existed separately, then even close up we would hardly notice it. But we are lucky, because most exist in dual systems. They are easy to find, since the black hole will pull the mass of its neighbor and influence it with gravity. The “pulled out” material forms an accretion disk, in which everything heats up and therefore creates strong radiation.

Let's assume you managed to find a binary system. How do you understand that a compact object is a black hole? Again we turn to the masses. To do this, measure the orbital speed of a nearby star. If the mass is incredibly huge with such small dimensions, then there are no more options left.

This is a complex mechanism. Stephen Hawking raised a similar topic back in the 1970s. He said that black holes are not really “black.” There are quantum mechanical effects that cause it to create radiation. Gradually the hole begins to shrink. The rate of radiation increases with decreasing mass, so the hole emits more and more and accelerates the process of contraction until it dissolves.

However, this is only a theoretical scheme, because no one can say exactly what happens at the last stage. Some people think that a small but stable trace remains. Modern theories have not yet come up with anything better. But the process itself is incredible and complex. It is necessary to calculate parameters in curved space-time, and the results themselves cannot be verified under normal conditions.

The Law of Conservation of Energy can be used here, but only for short durations. The universe can create energy and mass from scratch, but they must quickly disappear. One of the manifestations is vacuum fluctuations. Pairs of particles and antiparticles grow out of nowhere, exist for a certain short period of time and die in mutual destruction. When they appear, the energy balance is disrupted, but everything is restored after disappearance. It seems fantastic, but this mechanism has been confirmed experimentally.

Let's say one of the vacuum fluctuations acts near the horizon of a black hole. Perhaps one of the particles falls in, and the second runs away. The one who escapes takes some of the energy of the hole with her and can fall into the eyes of the observer. It will seem to him that a dark object has simply released a particle. But the process repeats itself, and we see a continuous stream of radiation from the black hole.

We've already said that Kirill feels like you need infinity to step over the horizon line. In addition, it was mentioned that black holes evaporate after a finite period of time. So, when you reach the horizon, the hole will disappear?

No. When we described Kirill's observations, we did not talk about the evaporation process. But, if this process is present, then everything changes. Your friend will see you flying across the horizon at the exact moment of evaporation. Why?

An optical illusion dominates Kirill. The emitted light in the event horizon takes a long time to reach its friend. If the hole lasts forever, then the light can travel indefinitely, and Kirill will not wait for the transition. But, if the hole has evaporated, then nothing will stop the light, and it will reach the guy at the moment of the explosion of radiation. But you don’t care anymore, because you died in the singularity long ago.

The formulas of the general theory of relativity have an interesting feature - symmetry in time. For example, in any equation you can imagine that time flows backwards and get a different, but still correct, solution. If we apply this principle to black holes, then a white hole is born.

A black hole is a defined area from which nothing can escape. But the second option is a white hole into which nothing can fall. In fact, she pushes everything away. Although, from a mathematical point of view, everything looks smooth, this does not prove their existence in nature. Most likely, there are none, and there is no way to find out.

Up to this point we have talked about the classics of black holes. They do not rotate and have no electrical charge. But in the opposite version, the most interesting thing begins. For example, you can get inside but avoid the singularity. Moreover, its “inside” is capable of contacting a white hole. That is, you will find yourself in a kind of tunnel, where the black hole is the entrance and the white hole is the exit. This combination is called a wormhole.

Interestingly, a white hole can be located anywhere, even in another Universe. If we know how to control such wormholes, then we will provide fast transportation to any area of ​​​​space. And even cooler is the possibility of time travel.

But don't pack your backpack until you know a few things. Unfortunately, there is a high probability that there are no such formations. We have already said that white holes are a conclusion from mathematical formulas, and not a real and confirmed object. And all observed black holes create matter falling and do not form wormholes. And the final stop is the singularity.

Black holes are one of the strangest phenomena in the Universe. In any case, at this stage of human development. This is an object with infinite mass and density, and therefore attraction, beyond which even light cannot escape - therefore the hole is black. A supermassive black hole can suck in an entire galaxy without choking, and beyond the event horizon, normal physics begins to screech and twist into a knot. On the other hand, black holes can become potential transition “holes” from one node of space to another. The question is, how close can we get to a black hole, and will there be consequences?

The supermassive black hole Sagittarius A*, located at the center of our galaxy, not only sucks in nearby objects, but also emits powerful radio emission. Scientists have long tried to discern these rays, but they were hampered by the scattered light surrounding the hole. Finally, they were able to break through the light noise using 13 telescopes, which were combined into a single powerful system. Subsequently, they discovered interesting information about the previously mysterious rays.

A few days ago, on March 14, one of the most outstanding physicists of our time left this world,

In order for a black hole to form, it is necessary to compress a body to a certain critical density so that the radius of the compressed body is equal to its gravitational radius. The value of this critical density is inversely proportional to the square of the black hole's mass.

For a typical stellar mass black hole ( M=10M sun) gravitational radius is 30 km, and the critical density is 2·10 14 g/cm 3, that is, two hundred million tons per cubic centimeter. This density is very high compared to the average density of the Earth (5.5 g/cm3), it is equal to the density of the substance of the atomic nucleus.

For a black hole at the galactic core ( M=10 10 M sun) gravitational radius is 3·10 15 cm = 200 AU, which is five times the distance from the Sun to Pluto (1 astronomical unit - the average distance from the Earth to the Sun - is equal to 150 million km or 1.5·10 13 cm). The critical density in this case is equal to 0.2·10 –3 g/cm 3 , which is several times less than the density of air, equal to 1.3·10 –3 g/cm 3 (!).

For the Earth ( M=3·10 –6 M sun), the gravitational radius is close to 9 mm, and the corresponding critical density is monstrously high: ρ cr = 2·10 27 g/cm 3, which is 13 orders of magnitude higher than the density of the atomic nucleus.

If we take some imaginary spherical press and compress the Earth, maintaining its mass, then when we reduce the radius of the Earth (6370 km) by four times, its second escape velocity will double and become equal to 22.4 km/s. If we compress the Earth so that its radius becomes approximately 9 mm, then the second cosmic velocity will take on a value equal to the speed of light c= 300000 km/s.

Further, a press will not be needed - the Earth, compressed to such a size, will already compress itself. In the end, a black hole will form in place of the Earth, the radius of the event horizon of which will be close to 9 mm (if we neglect the rotation of the resulting black hole). In real conditions, of course, there is no super-powerful press - gravity “works”. This is why black holes can only form when the interiors of very massive stars collapse, in which gravity is strong enough to compress matter to a critical density.

Evolution of stars

Black holes form at the final stages of the evolution of massive stars. In the depths of ordinary stars, thermonuclear reactions occur, enormous energy is released and a high temperature is maintained (tens and hundreds of millions of degrees). Gravitational forces tend to compress the star, and the pressure forces of hot gas and radiation resist this compression. Therefore, the star is in hydrostatic equilibrium.

In addition, a star can exist in thermal equilibrium, when the energy release due to thermonuclear reactions at its center is exactly equal to the power emitted by the star from the surface. As the star contracts and expands, the thermal equilibrium is disrupted. If the star is stationary, then its equilibrium is established in such a way that the negative potential energy of the star (the energy of gravitational compression) in absolute value is always twice the thermal energy. Because of this, the star has an amazing property - negative heat capacity. Ordinary bodies have a positive heat capacity: a heated piece of iron, cooling down, that is, losing energy, lowers its temperature. For a star, the opposite is true: the more energy it loses in the form of radiation, the higher the temperature at its center becomes.

This strange, at first glance, feature has a simple explanation: the star, as it radiates, slowly contracts. During compression, potential energy is converted into kinetic energy of falling layers of the star, and its interior heats up. Moreover, the thermal energy acquired by the star as a result of compression is twice as much as the energy lost in the form of radiation. As a result, the temperature of the star’s interior increases, and continuous thermonuclear synthesis of chemical elements occurs. For example, the reaction of converting hydrogen into helium in the current Sun occurs at a temperature of 15 million degrees. When, after 4 billion years, in the center of the Sun, all hydrogen turns into helium, for the further synthesis of carbon atoms from helium atoms, a significantly higher temperature will be required, about 100 million degrees (the electrical charge of helium nuclei is twice that of hydrogen nuclei, and to bring the nuclei closer together helium at a distance of 10–13 cm requires a much higher temperature). It is precisely this temperature that will be ensured due to the negative heat capacity of the Sun by the time the thermonuclear reaction of converting helium into carbon is ignited in its depths.

White dwarfs

If the mass of the star is small, so that the mass of its core affected by thermonuclear transformations is less than 1.4 M sun, thermonuclear fusion of chemical elements may cease due to the so-called degeneracy of the electron gas in the star's core. In particular, the pressure of a degenerate gas depends on density, but does not depend on temperature, since the energy of quantum motions of electrons is much greater than the energy of their thermal motion.

The high pressure of the degenerate electron gas effectively counteracts the forces of gravitational compression. Since pressure does not depend on temperature, the loss of energy by a star in the form of radiation does not lead to compression of its core. Consequently, gravitational energy is not released as additional heat. Therefore, the temperature in the evolving degenerate core does not increase, which leads to the interruption of the chain of thermonuclear reactions.

The outer hydrogen shell, unaffected by thermonuclear reactions, separates from the star's core and forms a planetary nebula, glowing in the emission lines of hydrogen, helium and other elements. The central compact and relatively hot core of an evolved low-mass star is a white dwarf - an object with a radius on the order of the Earth's radius (~10 4 km), a mass of less than 1.4 M sun and an average density of about a ton per cubic centimeter. White dwarfs are observed in large numbers. Their total number in the Galaxy reaches 10 10, that is, about 10% of the total mass of the observable matter of the Galaxy.

Thermonuclear burning in a degenerate white dwarf can be unstable and lead to a nuclear explosion of a sufficiently massive white dwarf with a mass close to the so-called Chandrasekhar limit (1.4 M sun). Such explosions look like Type I supernovae, which have no hydrogen lines in their spectrum, but only lines of helium, carbon, oxygen and other heavy elements.

Neutron stars

If the star’s core is degenerate, then as its mass approaches the limit of 1.4 M sun, the usual degeneracy of the electron gas in the nucleus is replaced by the so-called relativistic degeneracy.

The quantum motions of degenerate electrons become so fast that their speeds approach the speed of light. In this case, the elasticity of the gas decreases, its ability to counteract the forces of gravity decreases, and the star experiences gravitational collapse. During collapse, electrons are captured by protons, and neutronization of the substance occurs. This leads to the formation of a neutron star from a massive degenerate core.

If the initial mass of the star's core exceeds 1.4 M sun, then a high temperature is reached in the core, and electron degeneration does not occur throughout its evolution. In this case, negative heat capacity works: as the star loses energy in the form of radiation, the temperature in its depths increases, and there is a continuous chain of thermonuclear reactions converting hydrogen into helium, helium into carbon, carbon into oxygen, and so on, up to the elements of the iron group. The reaction of thermonuclear fusion of nuclei of elements heavier than iron no longer occurs with the release, but with the absorption of energy. Therefore, if the mass of the star's core, consisting mainly of iron group elements, exceeds the Chandrasekhar limit of 1.4 M sun , but less than the so-called Oppenheimer–Volkov limit ~3 M sun, then at the end of the nuclear evolution of the star, gravitational collapse of the core occurs, as a result of which the outer hydrogen shell of the star is shed, which is observed as a type II supernova explosion, in the spectrum of which powerful hydrogen lines are observed.

The collapse of the iron core leads to the formation of a neutron star.

When the massive core of a star that has reached a late stage of evolution is compressed, the temperature rises to gigantic values ​​of the order of a billion degrees, when the nuclei of atoms begin to break apart into neutrons and protons. Protons absorb electrons and turn into neutrons, emitting neutrinos. Neutrons, according to the quantum mechanical Pauli principle, with strong compression begin to effectively repel each other.

When the mass of the collapsing core is less than 3 M sun, neutron speeds are significantly less than the speed of light and the elasticity of matter due to the effective repulsion of neutrons can balance the gravitational forces and lead to the formation of a stable neutron star.

The possibility of the existence of neutron stars was first predicted in 1932 by the outstanding Soviet physicist Landau immediately after the discovery of the neutron in laboratory experiments. The radius of a neutron star is close to 10 km, its average density is hundreds of millions of tons per cubic centimeter.

When the mass of the collapsing stellar core is greater than 3 M sun, then, according to existing ideas, the resulting neutron star, cooling, collapses into a black hole. The collapse of a neutron star into a black hole is also facilitated by the reverse fall of part of the star's shell, ejected during a supernova explosion.

A neutron star typically rotates rapidly because the normal star that gave birth to it can have significant angular momentum. When the core of a star collapses into a neutron star, the characteristic dimensions of the star decrease from R= 10 5 –10 6 km to R≈ 10 km. As the size of a star decreases, its moment of inertia decreases. To maintain angular momentum, the speed of axial rotation must increase sharply. For example, if the Sun, rotating with a period of about a month, is compressed to the size of a neutron star, then the rotation period will decrease to 10 –3 seconds.

Single neutron stars with a strong magnetic field manifest themselves as radio pulsars - sources of strictly periodic pulses of radio emission that arise when the energy of the rapid rotation of a neutron star is converted into directed radio emission. In binary systems, accreting neutron stars exhibit the phenomenon of X-ray pulsar and type 1 X-ray burster.

One cannot expect strictly periodic pulsations of radiation from a black hole, since the black hole has no observable surface and no magnetic field. As physicists often say, black holes do not have “hair” - all fields and all inhomogeneities near the event horizon are emitted when the black hole is formed from collapsing matter in the form of a stream of gravitational waves. As a result, the resulting black hole has only three characteristics: mass, angular momentum and electric charge. All individual properties of the collapsing substance are forgotten when a black hole is formed: for example, black holes formed from iron and from water have, other things being equal, the same characteristics.

As predicted by the General Theory of Relativity (GR), stars whose iron core masses at the end of their evolution exceed 3 M sun, experience unlimited compression (relativistic collapse) with the formation of a black hole. This is explained by the fact that in general relativity the gravitational forces tending to compress a star are determined by the energy density, and at the enormous densities of matter achieved during the compression of such a massive star core, the main contribution to the energy density is no longer made by the rest energy of the particles, but by the energy of their movement and interaction . It turns out that in general relativity the pressure of a substance at very high densities seems to “weigh” itself: the greater the pressure, the greater the energy density and, consequently, the greater the gravitational forces tending to compress the substance. In addition, under strong gravitational fields, the effects of space-time curvature become fundamentally important, which also contributes to the unlimited compression of the star’s core and its transformation into a black hole (Fig. 3).

In conclusion, we note that black holes formed in our era (for example, the black hole in the Cygnus X-1 system), strictly speaking, are not one hundred percent black holes, since due to relativistic time dilation for a distant observer, their event horizons still have not formed. The surfaces of such collapsing stars appear to an observer on Earth as frozen, endlessly approaching their event horizons.

In order for black holes from such collapsing objects to finally form, we must wait the entire infinitely long time of the existence of our Universe. It should be emphasized, however, that already in the first seconds of relativistic collapse, the surface of the collapsing star for an observer from Earth approaches very close to the event horizon, and all processes on this surface slow down infinitely.