Wormholes in space. Astronomical hypotheses
(English)Russian Einstein's equations, which in turn are understood as an integral part of the maximally extended version of the Schwarzschild metric, describing eternal a black hole that does not change or rotate. Wherein, " maximally expanded" refers to the fact that spacetime should not have any " edges": for any possible trajectory of free fall of a particle (following geodesic (English)Russian) in space-time it should be possible to continue this path arbitrarily far into the future or past of the particle, except in cases where the trajectory falls into a gravitational singularity, as if it were in the center of the interior of a black hole. To satisfy this requirement, it turns out that in addition to the interior region of the black hole into which particles enter when they cross the event horizon from the outside, there must be a separate interior region of the white hole that allows one to extrapolate the particle trajectories that an outside observer would see standing in the distance from the event horizon. And just as there are two separate inner regions of spacetime, there are two separate outer regions, which are sometimes called two different " universes", the presence of a second Universe allows us to extrapolate some possible particle trajectories in the two inner regions. This means that the interior of a black hole can contain a mixture of particles that fall into it from any Universe (thus, an observer who sees light from one Universe can see light from another Universe), and particles from the interior of a white hole can escape to any Universe. All four regions can be seen on the Kruskal–Szekeres space-time diagram.Write a review of the article "Einstein-Rosen Bridge"
Links
- Winter K.. Roscosmos TV studio (November 12, 2011).
- (English) . Scientific American, a Division of Nature America, Inc (September 15, 1997).
- Visser M. General Interest Articles (English). Victoria University of Wellington, New Zealand (3 October 1996).
- Ideas Based On What We'd Like To Achieve (English). NASA.gov.
- Rodrigo E.(English) (2005).
- Müller Th. Institut für Visualisierung und Interaktive Systeme (English). Universität Stuttgart.
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An excerpt characterizing the Einstein-Rosen Bridge
“You’re all about attacking, but you don’t see that we don’t know how to do complex maneuvers,” he said to Miloradovich, who asked to go forward.“They didn’t know how to take Murat alive in the morning and arrive at the place on time: now there’s nothing to do!” - he answered the other.
When Kutuzov was informed that in the rear of the French, where, according to the Cossacks’ reports, there had been no one before, there were now two battalions of Poles, he glanced back at Yermolov (he had not spoken to him since yesterday).
“They ask for an offensive, they propose various projects, but as soon as you get down to business, nothing is ready, and the forewarned enemy takes his own measures.”
Ermolov narrowed his eyes and smiled slightly when he heard these words. He realized that the storm had passed for him and that Kutuzov would limit himself to this hint.
“He’s having fun at my expense,” Ermolov said quietly, nudging Raevsky, who was standing next to him, with his knee.
Soon after this, Ermolov moved forward to Kutuzov and respectfully reported:
- Time has not been lost, your lordship, the enemy has not left. What if you order an attack? Otherwise the guards won’t even see the smoke.
Kutuzov said nothing, but when he was informed that Murat’s troops were retreating, he ordered an offensive; but every hundred steps he stopped for three quarters of an hour.
The whole battle consisted only in what Orlov Denisov’s Cossacks did; the rest of the troops only lost several hundred people in vain.
As a result of this battle, Kutuzov received a diamond badge, Bennigsen also received diamonds and a hundred thousand rubles, others, according to their ranks, also received a lot of pleasant things, and after this battle even new movements were made at headquarters.
“This is how we always do things, everything is topsy-turvy!” - Russian officers and generals said after the Tarutino battle, - exactly the same as they say now, making it feel like someone stupid is doing it this way, inside out, but we wouldn’t do it that way. But people who say this either do not know the matter they are talking about or are deliberately deceiving themselves. Every battle - Tarutino, Borodino, Austerlitz - is not carried out as its managers intended. This is an essential condition.
An innumerable number of free forces (for nowhere is a person freer than during a battle, where it is a matter of life and death) influences the direction of the battle, and this direction can never be known in advance and never coincides with the direction of any one force.
If many, simultaneously and variously directed forces act on some body, then the direction of movement of this body cannot coincide with any of the forces; and there will always be an average, shortest direction, what in mechanics is expressed by the diagonal of a parallelogram of forces.
If in the descriptions of historians, especially French ones, we find that their wars and battles are carried out according to a certain plan in advance, then the only conclusion that we can draw from this is that these descriptions are not true.
The Tarutino battle, obviously, did not achieve the goal that Tol had in mind: in order to bring troops into action according to disposition, and the one that Count Orlov could have had; to capture Murat, or the goals of instantly exterminating the entire corps, which Bennigsen and other persons could have, or the goals of an officer who wanted to get involved and distinguish himself, or a Cossack who wanted to acquire more booty than he acquired, etc. But , if the goal was what actually happened, and what was a common desire for all Russian people then (the expulsion of the French from Russia and the extermination of their army), then it will be completely clear that the Tarutino battle, precisely because of its inconsistencies, was the same , which was needed during that period of the campaign. It is difficult and impossible to imagine any outcome of this battle that would be more expedient than the one it had. With the least tension, with the greatest confusion and with the most insignificant loss, the greatest results of the entire campaign were achieved, the transition from retreat to offensive was made, the weakness of the French was exposed and the impetus that Napoleon’s army had only been waiting for to begin their flight was given.
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 journeys 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 and 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 details, 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 that briefly connects regions separated by hundreds of thousands of light years, or, say, eras distant 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, 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 the 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 believe 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), 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 and Rosen’s “bridges,” and without them there is nothing to do in the microworld. For known values of the masses and charges of particles (electrons or protons), the Einstein Rosen bridge is not formed at all; instead, the “electric” solution predicts the so-called “naked” 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” - the 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 1950–1960s. 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 thought of as an impenetrable wormhole. ReisnerNordström's black hole is more complex, but also impenetrable. However, it is not so difficult to invent and describe traversable four-dimensional wormholes by selecting the desired type of metric (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 the same number of 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 that everything is there - the hole can be a time machine, 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 prevent 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 like 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 characterizing 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 this is how humans are designed, and scientists are no exception: if a barrier exists, there will always be those 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, this summer we will return, 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 (if, of course, we assume that the hole is stable or that we are able to maintain its “functionality”).
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 this 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, 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 the 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 when compressed, the rotation only accelerates, especially when collapsing 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 are reminiscent of other unusual objects predicted by modern physics, the cosmic strings that were formed (according to some theories) in the early Universe when superdense matter cooled and changed 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?
If spacetime 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 shortened word “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 burrows exist in interstellar or intergalactic space, if only because of the concentration of the same dark energy that accelerates the expansion of the Universe. There is no clear answer to the questions of 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
Einstein-Rosen Bridge
A 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 that approaches at a distance less than this radius will inevitably be sucked into the black hole and will not be able to escape. A person unlucky 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 most distant visible point).
Secondly, anyone who finds themselves within the Schwarzschild radius will discover a “mirror universe” on the “other side” of space-time (Fig. 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 be torn away from atoms, and even protons and neutrons in the nucleus will be scattered in different directions. In addition, to penetrate another universe, the probe would need to travel faster than the speed of light, and this is impossible. Thus, although the mirror universe is mathematically necessary for understanding the Schwarzschild solution, it will never be physically observable.
Rice. 10.2. The Einstein-Rosen Bridge connects two different universes. Einstein believed that any rocket that ended up on this bridge would be destroyed, which means that communication between these two universes is impossible. But later calculations showed that traveling on the platform, although extremely difficult, was still possible.
As a result, the famous Einstein-Rosen bridge connecting two universes (the bridge is named after Einstein and his co-author Nathan Rosen) is considered a mathematical oddity. This bridge is necessary to obtain a mathematically consistent theory of black holes, but it is impossible to get to 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 an interesting but forgotten application to the theory of relativity.
The situation began to change with the advent of the work of 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 figure skater whose speed increases as he presses his arms closer, the star will inevitably spin faster as it collapses. Thus, Schwarzschild's stationary solution for black holes was not the most physically relevant solution to Einstein's equations.
Kerr's proposed solution became a sensation in matters of relativity. Astrophysicist Subramanian 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, provides an absolutely accurate representation of the countless massive black holes that fill the universe . This “awe of beauty,” this incredible fact that the discovery that led to the search for beauty in mathematics found its exact counterpart in Nature, convinces me that beauty is something to which the human mind responds at the deepest, most meaningful level.
However, Kerr discovered that the massive rotating star was not compressed into a point. Instead, the rotating star is flattened until it eventually becomes 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 a “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 rather unexpected conclusion from Kerr's solution means that any space probe launched into a rotating black hole along its axis of rotation could in principle survive the enormous but finite influence of the gravitational fields at the center and make it all the way to the mirror Universe, avoiding death under the influence of the infinite curvature. The Einstein-Rosen Bridge acts as a tunnel connecting two regions of spacetime; this is a “wormhole” or “mole hole”. Thus, the Kerr black hole is a gateway to another universe.
Now imagine that our rocket ends 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 catastrophic collision awaits a rocket descending towards the black hole from the north pole. But as we approach the ring, the light from the mirror Universe reaches our sensors. Since all electromagnetic radiation, including from radars, moves in the orbit of a black hole, signals appear on our radar screens that repeatedly pass around the black hole. An effect is created that is reminiscent of a mirrored “chamber of laughter”, where we are misled by numerous reflections from all sides. The light bounces off multiple mirrors, creating the illusion that the room is full of replicas of ourselves.
Although Einstein believed that black holes were too incredible a phenomenon to exist in nature, he later, ironically, 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 digging into the ground, they create a shorter, alternate path between two points. These portals are also sometimes called portals or "gateways" to other dimensions. Whatever you call them, they may someday become a means of traveling between different dimensions, but this is an extreme case.
The first person 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. Since 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 a 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 with a lasso wrapped around it, 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 tightened to the circumference of the compressed donut, that is, to the circumference of the “hole”.
Mathematicians reveled in the fact that they had discovered 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 theory, dating back to Newton's time, 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 of thinking of the electron (which was usually thought of as a tiny dot with no structure) as a black hole. Thus, it was possible to use general relativity to explain the mysteries of the quantum world in unified field theory. They started with a solution for a standard black hole, which resembles a large vase with a long neck. They then cut off the neck and connected it to another partial solution to the black hole equations, that is, a vase that was turned upside down. According to Einstein, this bizarre but balanced configuration would be free of 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 move freely around the Universe until we accidentally fall into a black hole, where we are immediately pulled through a portal and emerge on the other side (after going through the “white” hole).
For Einstein, any solution to his equations, if it started from a physically plausible starting point, had to be related to a physically plausible object. But he wasn't worried about who would fall into the black hole and end up in a parallel universe. 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 could cross it fast enough to reach the other side.) According to Einstein, although portals were possible, a living thing could never go through any of them and talk about your experiences during this journey.
Einstein-Rosen Bridge. At the center of a black hole there is a “neck” that connects to the space-time of another universe or another point in our universe. While traveling through a stationary black hole would have fatal consequences, rotating black holes have a ring-shaped singularity that would allow passage through the ring and the Einstein-Rosen bridge, although this is still at the speculative stage.
