For publication work with the basic equations of general relativity (GR). Later it became clear that the new theory of gravity, which turns 100 years old in 2015, predicts the existence of black holes and space-time tunnels. Lenta.ru will tell about them.

What is OTO

General relativity is based on the principles of equivalence and general covariance. The first (weak principle) means the proportionality of inert (associated with motion) and gravitational (associated with gravitation) masses and allows (strong principle) in a limited area of ​​space not to distinguish between the gravitational field and motion with acceleration. A classic example is the elevator. With its uniformly accelerated upward movement relative to the Earth, the observer located in it is not able to determine whether he is in a stronger gravitational field or moves in a man-made object.

The second principle (general covariance) assumes that the GR equations retain their form when transforming the special theory of relativity created by Einstein and other physicists by 1905. The ideas of equivalence and covariance led to the need to consider a single space-time, which is curved in the presence of massive objects. This distinguishes general relativity from Newton's classical theory of gravity, where space is always flat.

General relativity in four dimensions includes six independent partial differential equations. To solve them (finding an explicit form of the metric tensor describing the curvature of space-time), it is necessary to set the boundary and coordinate conditions, as well as the energy-momentum tensor. The latter describes the distribution of matter in space and, as a rule, is associated with the equation of state used in the theory. In addition, the GR equations allow the introduction of a cosmological constant (lambda term), which is often associated with dark energy and, probably, the scalar field corresponding to it.

Black holes

In 1916, the German mathematical physicist Karl Schwarzschild found the first solution to the GR equations. It describes the gravitational field created by a centrally symmetric mass distribution with zero electric charge. This solution contained the so-called gravitational radius of the body, which determines the size of an object with a spherically symmetric distribution of matter, which photons (quanta of the electromagnetic field moving at the speed of light) are not able to leave.

The Schwarzschild sphere defined in this way is identical to the concept of the event horizon, and the massive object limited by it is identical to the concept of a black hole. The perception of a body approaching it within the framework of general relativity differs depending on the position of the observer. For an observer connected with the body, reaching the Schwarzschild sphere will occur in a finite proper time. For an external observer, the approach of the body to the event horizon will take infinite time and will look like its unlimited fall onto the Schwarzschild sphere.

Soviet theoretical physicists also contributed to the theory of neutron stars. In the 1932 article "On the Theory of Stars", Lev Landau predicted the existence of neutron stars, and in the work "On the Sources of Stellar Energy", published in 1938 in the journal Nature, he suggested the existence of stars with a neutron core.

How do massive objects turn into black holes? The conservative and currently most recognized answer to this question was given in 1939 by theoretical physicists Robert Oppenheimer (in 1943 he became the scientific director of the Manhattan Project, under which the world's first atomic bomb was created in the United States) and his graduate student Hartland Snyder.

In the 1930s, astronomers became interested in the question of the future of a star if its interior ran out of nuclear fuel. For small stars like the Sun, evolution will lead to the transformation into white dwarfs, in which the gravitational contraction force is balanced by the electromagnetic repulsion of the electron-nuclear plasma. In heavier stars, gravity is stronger than electromagnetism, and neutron stars are formed. The core of such objects is made of a neutron liquid, and it is covered by a thin plasma layer of electrons and heavy nuclei.

Image: East News

The limit value of the mass of a white dwarf, which prevents it from turning into a neutron star, was first estimated in 1932 by the Indian astrophysicist Subramanyan Chandrasekhar. This parameter is calculated from the equilibrium condition for the degenerate electron gas and gravitational forces. The current value of the Chandrasekhar limit is estimated at 1.4 solar masses.

The upper limit on the mass of a neutron star, at which it does not turn into a black hole, is called the Oppenheimer-Volkov limit. It is determined from the equilibrium condition for the degenerate neutron gas pressure and gravitational forces. In 1939, a value of 0.7 solar masses was obtained, modern estimates vary from 1.5 to 3.0.

Mole Hole

Physically, a wormhole (wormhole) is a tunnel connecting two distant regions of space-time. These areas can be in the same universe or link different points of different universes (within the framework of the multiverse concept). Depending on the ability to return through the hole, they are divided into passable and impassable. Impassable holes quickly close and do not allow a potential traveler to make the return trip.

From a mathematical point of view, a wormhole is a hypothetical object obtained as a special non-singular (finite and having a physical meaning) solution of the GR equations. Wormholes are usually depicted as a bent two-dimensional surface. You can get from one side of it to the other both in the usual way and through the tunnel connecting them. In the visual case of a two-dimensional space, it can be seen that this can significantly reduce the distance.

In 2D, wormhole throats - the openings from which the tunnel begins and ends - have the shape of a circle. In three dimensions, the mouth of a wormhole looks like a sphere. Such objects are formed from two singularities in different regions of space-time, which in hyperspace (space of higher dimension) are drawn together to form a hole. Since the hole is a space-time tunnel, you can travel through it not only in space, but also in time.

For the first time solutions of GR equations of the wormhole type were given in 1916 by Ludwig Flamm. His work, which described a wormhole with a spherical neck without gravitating matter, did not attract the attention of scientists. In 1935, Einstein and the American-Israeli theoretical physicist Nathan Rosen, unfamiliar with Flamm's work, found a similar solution to the GR equations. They were driven in this work by the desire to combine gravity with electromagnetism and get rid of the singularities of the Schwarzschild solution.

In 1962, American physicists John Wheeler and Robert Fuller showed that the Flamm wormhole and the Einstein-Rosen bridge collapse rapidly and are therefore impassable. The first solution to the GR equations with a traversable wormhole was proposed in 1986 by the American physicist Kip Thorne. Its wormhole is filled with matter with a negative average mass density that prevents the tunnel from closing. Elementary particles with such properties are still unknown to science. Probably, they can be part of dark matter.

Gravity today

The Schwarzschild solution is the simplest for black holes. Rotating and charged black holes have already been described. A consistent mathematical theory of black holes and related singularities was developed in the work of the British mathematician and physicist Roger Penrose. As early as 1965, he published an article in the journal Physical Review Letters titled "Gravity Collapse and Space-Time Singularities".

It describes the formation of the so-called trap surface, leading to the evolution of a star into a black hole and the emergence of a singularity - a feature of space-time, where the GR equations give solutions that are incorrect from a physical point of view. Penrose's conclusions are considered the first major mathematically rigorous result of general relativity.

Shortly thereafter, the scientist, together with Briton Stephen Hawking, showed that in the distant past the universe was in a state of infinite mass density. The singularities that arise in general relativity and are described in the works of Penrose and Hawking defy explanation in modern physics. In particular, this leads to the impossibility of describing nature before the Big Bang without involving additional hypotheses and theories, for example, quantum mechanics and string theory. The development of the theory of wormholes is also currently impossible without quantum mechanics.

Although Einstein believed that black holes were too incredible and could not exist in nature, later, ironically, he showed that they are even more bizarre than anyone could have imagined. Einstein explained the possibility of the existence of space-time "portals" in the depths of black holes. Physicists call these portals wormholes because, like a worm that bites into the ground, they create a shorter alternative path between two points. These portals are also sometimes referred to as portals or "gates" to other dimensions. Whatever you call them, someday they may become a means of travel between different dimensions, but this is an extreme case.

The first to popularize the idea of ​​portals was Charles Dodgson, who wrote under the pseudonym Lewis Carroll. In Alice Through the Looking-Glass, he imagined a portal in the form of a mirror that connected the suburbs of Oxford and Wonderland. Because Dodgson was a mathematician and taught at Oxford, he was aware of these multiply connected spaces. By definition, a multiply connected space is such that the lasso in it cannot be contracted to the size of a point. Usually, any loop can be pulled to a point without any difficulty. But if we consider, for example, a donut around which a lasso is wound, we will see that the lasso will tighten this donut. When we begin to slowly tighten the loop, we will see that it cannot be compressed to the size of a point; at best, it can be pulled down to the circumference of a compressed donut, that is, to the circumference of the "hole".

Mathematicians enjoyed the fact that they managed to find an object that was completely useless in describing space. But in 1935, Einstein and his student Nathan Rosen introduced the theory of portals to the physical world. They tried to use the solution to the black hole problem as a model for elementary particles. Einstein himself never liked the Newtonian theory that the gravity of a particle tends to infinity as it approaches it. Einstein believed that this singularity should be eradicated because it makes no sense.

Einstein and Rosen had the original idea to represent the electron (usually thought of as a tiny dot with no structure) as a black hole. Thus, general relativity could be used to explain the mysteries of the quantum world in a unified field theory. They started with a solution for a standard black hole, which looks like a large vase with a long neck. Then they cut off the “neck” and connected it to another particular solution to the black hole equations, that is, to a vase that was turned upside down. According to Einstein, this bizarre but balanced configuration would be free from the singularity in the origin of the black hole and could act like an electron.

Unfortunately, Einstein's idea of ​​representing the electron as a black hole failed. But today, cosmologists suggest that the Einstein-Rosen bridge could serve as a "gateway" between the two universes. We can freely move around the universe until we accidentally fall into a black hole, where we are immediately dragged through the portal and we appear on the other side (after passing through the "white" hole).

For Einstein, any solution to his equations, if it started from a physically probable starting point, had to be related to a physically probable object. But he didn't worry about who would fall into the black hole and end up in a parallel universe. The tidal forces would increase indefinitely at the center, and the gravitational field would immediately tear apart the atoms of any object that had the misfortune of falling into the black hole. (The Einstein-Rosen Bridge does open in a fraction of a second, but it closes so quickly that no object can pass through it fast enough to reach the other side.) Einstein believed that although the existence of portals is possible, a living being can never go through any of them and tell about your experiences during this journey.

Einstein-Rosen Bridge. At the center of a black hole is a "throat" that connects to the space-time of another universe or another point in our universe. While traveling through a stationary black hole would be fatal, spinning black holes have an annular singularity that would allow passage through the ring and the Einstein-Rosen bridge, though this is still under conjecture.

Instinct tells us that our world is three-dimensional. Based on this idea, scientific hypotheses have been built for centuries. According to the eminent physicist Michio Kaku, this is the same prejudice as the belief of the ancient Egyptians that the Earth was flat. The book is devoted to the theory of hyperspace. The idea of ​​multidimensionality of space caused skepticism, was ridiculed, but is now recognized by many authoritative scientists. The significance of this theory lies in the fact that it is able to combine all known physical phenomena into a simple structure and lead scientists to the so-called theory of everything. However, there is almost no serious and accessible literature for non-specialists. Michio Kaku fills this gap, explaining from a scientific point of view the origin of the Earth, the existence of parallel universes, time travel, and many other seemingly fantastic phenomena.

However, Kerr found that a massive rotating star does not shrink into a point. Instead, the rotating star is flattened until it eventually turns into a ring with remarkable properties. If you launch a probe into a black hole from the side, it will hit this ring and be completely destroyed. The curvature of space-time remains infinite if you approach the ring from the side. So to speak, the center is still surrounded by the "ring of death". But if you launch a space probe into the ring from above or below, it will have to deal with a large but finite curvature; in other words, the gravitational force will not be infinite.

This highly unexpected conclusion from Kerr's solution means that any space probe launched into a spinning black hole along its rotational axis could, in principle, survive the huge but finite impact of gravitational fields at the center and make it all the way to the mirror universe, avoiding death under the influence of infinite curvature. The Einstein–Rosen Bridge acts as a tunnel connecting two regions of spacetime; this is the "wormhole", or "molehole". Thus, the Kerr black hole is a gateway to another universe.

Now let's imagine that our rocket ended up on the Einstein-Rosen bridge. As she approaches the spinning black hole, she sees a ring-shaped spinning star. At first, it seems that a rocket descending towards the black hole from the direction of the north pole is in for a catastrophic collision. But as we approach the ring, the light from the mirror universe reaches our sensors. Since all electromagnetic radiation, including from radars, orbits the black hole, signals appear on the screens of our radars that repeatedly pass around the black hole. An effect is created that resembles a mirrored “laughter room”, where we are misled by numerous reflections from all sides. The light ricochets off many mirrors, creating the illusion that the room is full of our replicas.

The same effect is observed when passing through a black hole according to Kerr. Because the same beam of light orbits the black hole many times, the radar in our rocket picks up images orbiting the black hole, creating the illusion of objects that aren't really there.

Einstein-Rosen Bridge

The relativistic description of black holes appears in the work of Karl Schwarzschild. In 1916, just a few months after Einstein wrote down his famous equations, Schwarzschild was able to find an exact solution for them and calculate the gravitational field of a massive stationary star.

Schwarzschild's solution had several interesting features. First, there is a “point of no return” around a black hole. Any object approaching at a distance less than this radius will inevitably be pulled into a black hole, and it will not be able to escape. A person unfortunate enough to be within the Schwarzschild radius will be captured by the black hole and crushed to death. Currently, this distance from the black hole is called Schwarzschild radius, or event horizon(the farthest visible point).

Second, anyone within the Schwarzschild radius will discover a "mirror universe" on the "other side" of space-time (Figure 10.2). Einstein was not bothered by the existence of this bizarre mirror universe, because communication with it was impossible. Any space probe sent to the center of a black hole will encounter infinite curvature; in other words, the gravitational field will be infinite, and any material object will be destroyed. Electrons will break away from atoms, and even protons and neutrons in the nucleus will be blown apart. In addition, to penetrate into another universe, the probe would need to fly faster than the speed of light, which is impossible. Thus, although the mirror universe is mathematically necessary for understanding the Schwarzschild solution, it will never be possible to physically observe it.

Rice. 10.2. The Einstein-Rosen bridge connects two different universes. Einstein believed that any rocket that landed on this bridge would be destroyed, which means that communication between these two universes is impossible. But later calculations showed that platform travel, although extremely difficult, is still possible.

As a result, the famous Einstein-Rosen bridge connecting the two universes (the bridge is named after Einstein and his co-inventor Nathan Rosen) is considered a mathematical quirk. This bridge is necessary to obtain a mathematically consistent theory of black holes, but it is impossible to get into the mirror universe via the Einstein-Rosen bridge. Einstein-Rosen bridges soon showed up in other solutions of gravitational equations, such as the Reisner-Nordström solution for a black hole with an electric charge ... Nevertheless, the Einstein-Rosen bridge remained a curious but forgotten application to the theory of relativity.

The situation began to change with the advent of the work of the New Zealand mathematician Roy Kerr, who in 1963 found another exact solution to Einstein's equations. Kerr believed that any collapsing star rotates. Like a spinning skater whose speed increases as he closes his arms, the star will inevitably spin faster as it collapses. Thus, the stationary Schwarzschild solution for black holes was not the most physically relevant solution to the Einstein equations.

Kerr's proposed solution became a sensation in matters of relativity. Astrophysicist Subramanyan Chandrasekhar once said:

The most stunning event in my entire scientific life, that is, more than forty-five years, was the realization that the exact solution of the equations of Einstein's general theory of relativity, discovered by the New Zealand mathematician Roy Kerr, gives an absolutely accurate representation of the countless massive black holes that fill the universe . This “awe of the beautiful”, this incredible fact that the discovery that the search for beauty in mathematics led to found its exact copy in Nature convinces me that beauty is something that the human mind responds to at the deepest, most meaningful level.

However, Kerr found that a massive rotating star does not shrink into a point. Instead, the rotating star is flattened until it eventually turns into a ring with remarkable properties. If you launch a probe into a black hole from the side, it will hit this ring and be completely destroyed. The curvature of space-time remains infinite if you approach the ring from the side. So to speak, the center is still surrounded by the "ring of death". But if you launch a space probe into the ring from above or below, it will have to deal with a large but finite curvature; in other words, the gravitational force will not be infinite.

This highly unexpected conclusion from Kerr's solution means that any space probe launched into a spinning black hole along its rotational axis could, in principle, survive the huge but finite impact of gravitational fields at the center and make it all the way to the mirror universe, avoiding death under the influence of infinite curvature. The Einstein-Rosen bridge acts as a tunnel connecting two regions of space-time; this is the "wormhole", or "molehole". Thus, the Kerr black hole is a gateway to another universe.

Now let's imagine that our rocket ended up on the Einstein-Rosen bridge. As she approaches the spinning black hole, she sees a ring-shaped spinning star. At first, it seems that a rocket descending towards the black hole from the north pole is in for a catastrophic collision. But as we approach the ring, the light from the mirror universe reaches our sensors. Since all electromagnetic radiation, including from radars, orbits the black hole, signals appear on the screens of our radars that repeatedly pass around the black hole. An effect is created that resembles a mirrored “laughter room”, where we are misled by numerous reflections from all sides. The light ricochets off many mirrors, creating the illusion that the room is full of our replicas.

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Links

• Winter K.. Roskosmos television studio (November 12, 2011).
• (English) . Scientific American, a Division of Nature America, Inc. (September 15, 1997).
• Visser M. General Interest Articles. Victoria University of Wellington, New Zealand (October 3, 1996).
• Ideas Based On What We'd Like To Achieve. NASA.gov.
• Rodrigo E.(English) (2005).
• Müller Th. Institut für Visualisierung und Interaktive Systeme. Universität Stuttgart.

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An excerpt characterizing the Einstein-Rosen Bridge