Characterized by infinite density and temperature of the substance. A cosmological singularity is one example of gravitational singularities predicted by general relativity (GR) and some other theories of gravity.
The emergence of this singularity when extending back in time any solution of general relativity that describes the dynamics of the expansion of the Universe was rigorously proven in 1967 by Stephen Hawking. He also wrote:
“The results of our observations confirm the assumption that the Universe arose at a certain point in time. However, the very moment of the beginning of creation, the singularity, does not obey any of the known laws of physics.”
For example, density and temperature cannot be simultaneously infinite, since at infinite density the measure of chaos tends to zero, which cannot be combined with infinite temperature. The problem of the existence of a cosmological singularity is one of the most serious problems of physical cosmology. The point is that none our knowledge of what happened after the Big Bang cannot give us no information about what happened before.
Attempts to solve the problem of the existence of this singularity are going in several directions: firstly, it is believed that quantum gravity will give a description of the dynamics of the gravitational field free from singularities, and secondly, there is an opinion that taking into account quantum effects in non-gravitational fields can violate the condition of energy dominance, on on which Hawking's proof is based, thirdly, modified theories of gravity are proposed in which the singularity does not arise, since extremely compressed matter begins to be pushed away by gravitational forces (the so-called gravitational repulsion), and not attracted to each other.
Notes
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- Clark, John D.
- Richard Tyler
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Cosmological singularity is a theoretical construction of a certain state in which the Universe was at the initial moment. The peculiarity of this state is that it is characterized by infinite density and at the same time infinite temperature.
The emergence of the concept
A cosmological singularity is a special case of a gravitational singularity. If we are accustomed to considering matter as some smooth and boundless space (manifold), then in the region of gravitational singularity space-time is curved. In 1915 - 1916, the great physicist Albert Einstein published his theory, according to which gravitational effects exist not as a consequence of the work of any forces arising between bodies or in fields, but as a result of the distortion of space-time itself. Using his equations, Einstein was able to describe the relationship between the curvature of space-time and the matter that is in it.
Later, in 1967, Stephen Hawking used Einstein's equations for general relativity, which describe the dynamics of the Universe, to obtain solutions for elapsed time. That is, he determined the state of the Universe at the initial moment of its existence, and proved that such a moment really exists.
Gravitational singularity
It is not yet possible to accurately describe the gravitational singularity for the reason that many known quantities within its limits tend to infinity or become uncertain. For example, the energy density of the chosen frame of reference for this region or the scalar curvature.
Thanks to the work of theoretical physicists, we have strict evidence that such a gravitational singularity must be located in the hearts of black holes, namely behind, otherwise the black hole simply would not have formed. Unfortunately, it is impossible in principle to observe anything beyond the event horizon, although there are suggestions that there are black holes whose singularity extends slightly beyond its limits and can be observed. The cosmological singularity is called “bare” because theoretically it could be seen.
Properties, paradoxes and consequences of cosmological singularity
The main characteristics of the singularity are simultaneously infinite temperature and density of matter. One can try to imagine such a phenomenon as the concentration of an infinitely large mass in an infinitely small volume. However, according to physical calculations, these two quantities cannot simultaneously tend to infinity. As is known, temperature is closely related to the measure of chaos, which can only decrease with increasing density, just like temperature itself.
It is reliably known that there is a certain moment in time at which the Universe was born from a singularity. But we cannot obtain any knowledge about what happened before the singularity from calculations or observations. Also, the central point, the core from which the Big Bang occurred, cannot be found. And most importantly, how the cosmological singularity gave birth to the unthinkable of our Universe.
Unfortunately, today the developed physical structures cannot explain the presence of such a phenomenon as singularity, since all existing laws of physics are not applicable in its area. As the famous modern physicist Michio Kaku said: “we call a singularity what we cannot understand.”
A new stage in the development of modern cosmology began after the work Friedman(1922).
Using the relativistic theory of gravity Einstein, he obtained a mathematical model of the movement of matter throughout the Universe under the influence of gravitational forces. Friedman proved that the matter of the Universe cannot be at rest, i.e. The Universe is non-stationary: it must either contract or expand. From theory Friedman it follows that our Universe arose from a state of cosmological singularity.
In 1948 Gamow, Alfer and Herman proposed the possibility of the emergence of a hot Universe as a result of the “Big Bang” of matter.
The main idea of the hot Universe hypothesis was that the processes of thermonuclear reactions at the very beginning of the expansion of the Universe after the explosion and as it further evolved led to the relationship between the amounts of various chemical elements and their isotopes observed in space at present.
Observations of various objects of the Universe: hot stars, large gas nebulae, giant molecular clouds, the Sun, cosmic rays, quasars, galaxies, etc. have shown that, by mass, 25 27% helium is found in them, 70 72% hydrogen and a small admixture of other chemical elements, the proportion of which varies from object to object, but the content of helium and hydrogen is constant.
But before the formation of celestial bodies (galaxies, stars, etc.), the matter of the Universe was homogeneous (all four force interactions represent one “superunion” at a temperature T10 32 K) and there were no pressure drops, therefore, there was no force , as a result of which rapid expansion began. The physical vacuum played a special role in this. Moreover, it can be different depending on the conditions.
In it along with energy density(due to the interaction of virtual particles) simultaneously arise tension(similar to the tension forces that arise when stretching, for example, a metal rod). These tensions are equivalent to negative pressure, i.e. as if negative pressure arises. In ordinary media, tension and pressure constitute a small fraction of the total energy density. In a physical vacuum, the negative pressure is enormous and in absolute value is equal to the energy density. As the Universe expands (temperature decreases), the symmetry between electromagnetic and weak interactions is broken. As is known, weak interaction is associated with the presence of special charges (different from electric charges, between which electromagnetic interaction occurs with the help of photons) and this interaction occurs at very short distances.
This is due, first of all, to the large mass of weak interaction carriers W + , W and Z o - bosons. However, at temperatures above T10 15 K, as calculations show, there is a single electroweak interaction between particles.
Its carriers W + , W and Z o - bosons and -photons are abundant and have no mass. Quarks and leptons have no mass. A few minutes after the expansion of the Universe, the temperature dropped to 10 9 K.
At such temperatures, it has already become possible to combine protons and neutrons to form deuterium nuclei, which, as a result of thermonuclear reactions, lead to the formation of nuclei of helium atoms.
But due to the continued expansion of the Universe and decreasing temperatures, the thermonuclear reactions of the early Universe stopped.
In 5 minutes, about 25% of helium had formed, and 75% was hydrogen. Indeed, numerous observations have shown that the first generation of stars in the Universe had exactly this percentage composition.
The nuclei of atoms of heavier elements appeared in the Universe many billions of years later as a result of nuclear reactions in the bowels of stars. All active processes involving elementary particles ended, and a long period of relatively quiet expansion of the Universe began.
The expanding substance was a high-temperature, ionized plasma, not transparent to photon radiation, which at that moment determined the pressure force.
In this mixture of plasma and radiation there were small fluctuations in the density of the substance - sound waves. After 310 5 years of the photon era, due to the continuing expansion of the Universe, the plasma cooled to 410 3 K and turned into a neutral gas in the process of capturing free electrons by the nuclei of atoms. This gas became transparent to photons, which received (discovered in 1965) the name relict radiation. Currently, the energy of relict photons has decreased, and the temperature of photon radiation is only 3 - 5 K. Relict radiation is weak radio noise coming from space, regardless of the direction of the receiving antenna. The number of cosmic microwave background photons located in every 1 cm 3 of the Universe is 500, and their energy density is 510 13 erg/cm 3 . Due to the absence of radiation pressure, the elasticity of the neutral gas dropped sharply and the manifestation of gravitational instability became possible, which led to the formation of rather large gas condensations. Due to the compaction of sound vibrations as they propagate in these lumps of gas, gravitational forces begin to increase, which leads to the formation of massive clouds, which further evolve into superclusters of galaxies, clusters of galaxies and galaxies.
Everything that is observed today in space is a manifestation of a cosmological singularity.
It is currently believed that there was no preliminary compression before the cosmological singularity; it became the source of time, and the singularity inside the black hole is the end of the streams of the river of time. Therefore, in a cosmological singularity, time and space also disintegrate into quanta. In this regard, the question itself loses its meaning: what happened even earlier? One can only note that near the singularity on the scale of time and space quanta, there was a “foam” of these quanta, i.e. quantum fluctuations of space and time were observed. At this time, small “virtual” closed worlds and virtual black and white holes are born and immediately disappear.
Such small dimensions at high energies of boiling “foam” made it possible for the existence of not three, but more dimensions. However, these additional dimensions remain twisted and are not realized, and only three spatial dimensions remain, which, with the expansion of matter, lead to the current state of the Universe.
Consequently, time in a singularity radically changes its quantum properties and the beginning of the expansion of the Universe is the source of our continuous flow of time, which flows in one direction: from the past to the future. It is known that the cosmological singularity occurred 15 - 20 billion years ago. During this time, the light emerging from any source, even at the moment of the beginning of expansion, will have time to travel a finite distance in the Universe of 1520 billion light years or about 610 15 pc. Therefore, points in the space of the Universe that lie at such distances from us are called the visibility horizon. Those areas of space that lie beyond the visibility horizon are fundamentally unobservable today, but near the visibility horizon we can observe matter from the distant past.
Because of the effect Doppler The red shift of light increases without limit when the emitting object approaches the visibility horizon. And on the horizon itself it is infinite, so we can only see a finite number of stars and galaxies in the Universe. In this regard, the paradox of classical cosmology is solved: photometric, which is as follows. Since the Universe is infinite, it is filled with an infinite number of stars and the line of sight will sooner or later encounter a luminous star. In this case, the entire sky should shine like the surface of the Sun or the surface of other stars. In reality, due to the presence of a visual horizon, we see a finite number of stars, which are sparsely scattered in space. Our night sky appears dark: chaotically scattered luminous points of stars are visible in it. Confirmation of the hot beginning of the emergence of our Universe are the results of observations of objects in outer space. These include, for example, the presence of cosmic microwave background radiation, the presence of 25 - 30% helium in the composition of the stellar matter of the early Universe.
We turn to the consideration of the most important issue of cosmology - the question of the beginning of cosmological expansion, the question of singularity. The general result of what was stated in the previous sections is that the Universe is expanding isotropically and homogeneously, starting at least from the moment when equality was satisfied and with a high degree of probability was described by the Friedman model much earlier, starting from the era of the synthesis of chemical elements, i.e. i.e. from the first seconds of expansion and from densities of the order
What happened even earlier? Did the Universe expand according to Friedmann, starting from the singularity (or at least from the “Planckian” moment, or was the early epoch essentially non-Friedmannian? Did the matter of the Universe pass through an infinitely greater density (or at least through the “Planckian” density or did the compression of the Universe in an even earlier epoch give way to expansion at finite density [see, for example, Alfven (1971)]?
According to Friedman's model, the expansion of the Universe began from a singularity. Since the 30s, for decades, cosmology has been wondering whether the presence of a singularity at the beginning of the expansion is a special property of the Friedmann model (and other fairly symmetric models); whether the singularity will disappear with the introduction of small peculiar velocities of matter motion or rotation?
The analogy with the mechanical problem of expanding a ball in Newton's theory supported such assumptions. Indeed, if we consider in Newton’s theory the expansion of gravitating particles simultaneously flying along radii from one point, then the expansion begins from a singularity. However, in the presence of small peculiar velocities, the points fly past each other near the Center, the particle density is always finite and there are no singularities
arise. Perhaps a similar situation is possible in the cosmological problem of Einstein’s theory?
It is important to note one circumstance here, which is emphasized by Lifshitz and Khalatnikov (1963a, b). If there was no singularity in the past and the observed expansion of the Universe in the past was preceded by compression, then the cosmological model describing the passage of matter through the maximum density and subsequent expansion should be stable, i.e., relate to the “general solution” in the terminology of Lifshitz and Khalatnikov. In other words, let there be some model without a singularity that describes the compression of matter to a finite density (without a singularity), and then its expansion, and let a small change in the parameters of the model during the compression phase lead to the emergence of a singularity. Then, obviously, this model cannot be implemented in reality, since there will always be random fluctuations that lead the model away from a solution without a singularity. Thus, a solution without a singularity must be neither exceptional nor degenerate, but general in order to qualify for a description of the real Universe.
However, if the expansion starts from the singularity, then the requirement of generality of the solution near the singularity is no longer necessary. Indeed, in this case, the initial conditions that determine the solution are set by some unknown processes at enormous curvatures of space-time, i.e., under conditions not described by modern theory. Perhaps the processes in this case lead to special initial conditions for the expansion of the Universe, for example, to almost complete homogeneity and isotropy [see Peebles (1971a)]. Therefore, even if it were possible to prove that the general solution does not contain a singularity, this would not mean that the expansion did not begin from the singularity.
So, cosmology was faced with two different questions: 1) is there a general (in the sense of “stable”) cosmological solution without a singularity? and 2) was there a singularity in the past under conditions found in the real Universe?
At the end of the 60s, a positive answer to the second question was given (Penrose, Hawking, Geroch). It was proven that the expansion of the Universe began from a singularity (if, of course, GTR is valid, but the change in GTR itself, if associated with large curvature, requires “almost” singularity), however, how exactly did the expansion proceed near the singularity - according to Friedman or more complex way - has not been established. After these works, the urgency of the first question for cosmology disappeared. Indeed, the structure of the solution near the singularity does not necessarily correspond to the general solution, and the problem arises: in some way
establish the true nature of the beginning of the expansion of the real Universe.
In 1972, after long work, Belinsky, Lifshits, Khalatnikov constructed a general (stable) solution with a singularity, i.e., they gave a positive answer to the first question.
In terms of its properties, the general solution turned out to be qualitatively the same as the solution near the singularity for the “mixed” world model (see §§ 4 and 5 of Chapter 21).
In our further presentation, we will focus on the proof of the presence of a singularity in the past in the Universe and on physical processes near the singularity itself. One can hope that in the future, an analysis of these processes and the consequences of them will make it possible to establish the true nature of the expansion of the Universe at the earliest stages, at densities significantly exceeding the nuclear one.
All of the above conclusions follow from the theory, as long as quantum phenomena occurring in a black hole are not taken into account. Let us assume that the observer is on the surface of a star experiencing gravitational collapse. When approaching the source of a strong gravitational field, tidal gravitational forces arise, which are experienced by any body with finite dimensions. This is due to the fact that strong gravitational fields are always heterogeneous in composition and therefore different points of such bodies are subject to unequal gravitational forces.
During the fall, the opposing pressure forces of the star's substance no longer provide any resistance to the growing force of gravity, so the surface of the star will reach the gravitational radius, cross it and will uncontrollably continue to shrink further.
Since the compression process cannot stop, then in a short period of time (according to the clock on the surface of the star) the star will shrink to a point, and the density of matter will become infinite, i.e. star reaches singular condition.
As the singular state approaches, tidal gravitational forces also tend to infinity. This means that any body will be torn apart by tidal forces. If the body is below the horizon, then it is impossible to avoid the singularity.
For a black hole, for example, with a mass of ten solar masses, the time it takes to fall into a singularity is only one hundred thousandth of a second. Any attempts to escape from a black hole will lead to a decrease in the time period for entering a singular state. The smaller the mass and size of the black hole, the greater the tidal forces on its horizon.
For example, for a black hole with a mass of a thousand solar masses, tidal forces correspond to a pressure of 100 atm. In the vicinity of a singular state, enormous tidal forces lead to changes in physical properties.
If we move from external space through the surface of the horizon into the black hole, then in the formulas describing four-dimensional space-time, the time coordinate is replaced by a radial spatial coordinate, i.e. time turns into a radial spatial distance, and this distance is time.
The distance from the horizon to the center of the black hole, of course, means that the period of time during which bodies can exist inside the black hole is finite. For example, for a black hole with a mass of 10 solar masses it is t » 10 - 4 s. Inside a black hole, all the arrows of time converge to a singularity, and any body will be destroyed, and space and time disintegrate into quanta.
Thus, the time quantum is characterized by the value t pl » 10 - 44 s, and the Planck length of the quantum pl » 10 - 33 cm.
Consequently, the continuous flow of time in the singularity consists of time quanta, just as the flow of water in a stream, when passing through a sieve, is broken into tiny droplets. In this regard, it makes no sense to ask what will happen next.
The concepts “earlier” and “later” completely lose their meaning: it is fundamentally impossible to divide a time quantum into even smaller parts, just as it is impossible, for example, to divide a photon into parts.
With the transition to quantum processes, the connection between energy and time becomes increasingly apparent.
However, in the future, when describing processes, we cannot do without the concept of physical vacuum and its quantum properties.
According to modern concepts, vacuum is not emptiness, but is a “sea” of all kinds of virtual particles and antiparticles that do not appear as real particles.
This vacuum “boils,” continuously generating pairs of virtual particles and antiparticles for a short time, which instantly disappear. They cannot turn into real particles and antiparticles.
According to the uncertainty relation Heisenberg, the product of the lifetime Dt of a virtual pair of particles and their energy DW is of the order of constant Plank h.
If any strong field (for example, electric, magnetic, etc.) is applied to the physical vacuum, then under the influence of its energy some virtual particles can become real, i.e. in a strong field, real particles are born from a physical vacuum due to the energy of this field.
For example, in a strong electric field, electrons and positrons are born from a vacuum. When studying the properties of the physical vacuum near a rotating black hole, it was theoretically proven that the birth of radiation quanta should occur due to the energy of the vortex gravitational field.
Since virtual particles and antiparticles are born in a vacuum at a certain distance from each other, in the case of the presence of a vortex gravitational field of a black hole, a particle can be born outside the horizon, and its antiparticle under the horizon. This means that a particle can fly into outer space, while the antiparticle will fall into a black hole.
Consequently, they can never reconnect and annihilate. Therefore, a stream of particles will appear in space, emitted by the black hole, which will carry away some of its energy. This will lead to a decrease in the mass and size of the black hole. This radiation process is similar to when the surface of a body is heated to a certain temperature.
Thus, for a black hole of 10 solar masses, the temperature is »10 - 8 K. The greater the mass of the black hole, the lower its temperature, and, conversely, the lower the mass, the higher the temperature. Thus, a black hole with a mass m "10 12 kg and the size of an atomic nucleus will have a quantum evaporation power of "10 10 W for "10 10 years at a temperature T" 10 11 K. When the mass of the black hole decreases to m "10 6 kg , and the temperature reaches T»10 15 K, the radiation process will lead to an explosion and in 0.1 s an amount of energy will be released comparable to the explosion of 10 6 megaton hydrogen bombs.
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