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Victor Berezin

Publications and source records attributed to Victor Berezin.

At least 19 recordsLinked to original sources
arXiv2025

The way to the Big Bang

We propose conformal invariance as a fundamental symmetry governing cosmological particle creation from vacuum fluctuations, employing a phenomenological approach with an ideal fluid action to address the long-standing back-reaction problem. We demonstrate that particle production cannot emerge from classical vacua but must originate from a quantum vacuum at zero scale factor, with the transition surface constituting a light-like rather than space-like hypersurface. This implies that particles are created on the light cone and remain causally connected, with their apparent simultaneity being illusory. Our model requires an open Universe ($k=0, -1$) and reconceptualizes the Big Bang as a detonation wave propagating through quantum vacuum at the speed of light.

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arXiv2024

Conformally Invariant Gravity and Gravitating Mirages

The action of an ideal fluid in Euler variables with a variable number of particles is used for the phenomenological description of the processes of particle creation in strong external fields. It has been demonstrated that the conformal invariance of the creation law imposes quite strict restrictions on the possible types of sources. It is shown that combinations with the particle number density in the creation law can be interpreted as dark matter within the framework of this model.

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arXiv2023

Conformal invariance, cosmological particle production and imitation of dark matter

Using a model for an ideal fluid with a variable number of particles, a phenomenological description of the processes of particle production in strong external fields is investigated. The conformal invariance of the creation law is shown, which imposes rather rigorous restrictions on the possible types of sources. It appears that the combinations with the particle number density can imitate dark matter within this model.

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arXiv2021

Double layers in Weyl geometry and some physical implications

In this thesis, we attempt to gain a more complete insight into Double Layer Theories in Weyl Gravity. In order to do this, we first establish the premise of Weyls Theory, including its provenance, development and flaws. This is all discussed in the first five chapters of the thesis. After having established Weyls Infinitesimal geometry and his gauged (scalar-tensor) gravity theory, we move onto the topic at hand, namely, Double Layers. We define the action to be used and describe the volume of integration (especially the Singular Hyper Surface) across which the action principle is setup. We define our gauss Normal Coordinate system and the scheme which we follow when we undertake our calculation. The following sections detail the variation process, in a succinct manner, taking turn by turn, each of the four parameters of our Quadratic Lagrangian. In the last chapter, we conclude the thesis by gleaning out the meaning behind our newfound surface energy tensor terms and what they might imply physically, as well as drawing a clearer picture of contrast between General Relativity and Weyl gravity.

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arXiv2019

Least action principle and gravitational double layer

The higher derivative gravitational theories exhibit new phenomena absent in General Relativity. One of them is the possible formation of the so called double layer which is the pure gravitational phenomenon and can be interpreted, in a sense, as the gravitational shock wave. In this paper we show how some very important features of the double layer equations of motion can be extracted straight from the least action principle.

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arXiv2018

Spherically symmetric double layers in Weyl+Einstein gravity

The main results are the following. We derived the matching conditions for the spherically symmetric singular hypersurface (in our case it is equivalent to the world line) in the Weyl$+$Einstein gravity. It was found, that the residual extrinsic curvature tensor of this surface must be continuous on the singular hypersurface. The result is the same as that found by Senovilla, it is dictated by the very possibility to have the double layer, but the jump in the normal derivative of the radius may be not zero. It was found that in the presence of the double layer, the matching conditions contain an arbitrary function, and this result is quite new and very important. One of the consequences of such freedom is that the trace of the extrinsic curvature tensor of the singular hypersurface is necessarily equal to zero. We suggested the physical interpretation for the $S_0^n$ and $S_n^n$ components of the surface matter energy-momentum tensor of the shell. In General Relativity they are zero by virtue of the Einstein equations. In the quadratic gravity they are not necessarily zero. Our interpretation is that these components describe the energy flow $(S^{0n})$ and the momentum transfer $(S^{nn})$ of the particles produced by the double layer itself. Moreover, the requirement of the zero trace of the extrinsic curvature tensor (mentioned above) implies that $S_n^n=0$, and this fact also support our suggestion, because it means that for the observer sitting on the shell, the particles will be seen created by pairs, and the sum of their momentum transfers must zero. We derived also the matching conditions for the null hypersurface, and this is, again, quite new. We found that the null-double layer in the Weyl$+$ Einstein gravity does not exist at all.

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arXiv2017

On the theory of spherically symmetric thin shells in conformal gravity

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy-momentum tensor of the thin shell is proportional to Dirac delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl+Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in details the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless (= massless) shells it is shown that their dynamics can not be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl+Einstein gravity the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

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arXiv2016

Particle creation phenomenology, Dirac sea and the induced Weyl and Einstein-dilaton gravity

We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the "usual" hydrodynamical description of the particle motion written in the Eulerian coordinates we substituted the particle number conservation law (which enters the formalism) by "the particle creation law", proportional to the square of the Weyl tensor (following the famous result by Ya.B.Zel`dovich and A. A.Starobinsky). Then, demanding the conformal invariance of the whole dynamical system, we have got both the (Weyl)-conformal gravity and the Einstein--Hilbert gravity action integral with dilaton field. Thus, we obtained something like the induced gravity suggested first by A. D.Sakharov. It is shown that the resulting system is self-consistent. We considered also the vacuum equations. It is shown that, beside the "empty vacuum", there may exist the "dynamical vacuum", which is nothing more but the Dirac sea.

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arXiv2014

On the phenomenological description of particle creation and its influence on the space-time metrics

The method is proposed for the phenomenological description of particle creation by external fields (in the presence of gravitational field or without it). It is shown that, despite the appearance of the non-dynamical degrees of freedom, such as the number density and four-velocities of particles at the moment of creation (and corresponding Lagrange multipliers) the theory is complete and self-consistent. It appears that the very existence of particle creation processes requires the non-zero trace anomaly of the external quantum field under consideration.

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arXiv2011

Could the real (not virtual) static observer exist outside a Schwarzschild black hole?

The aim of this Letter is rather pedagogical. We considered the static spherically symmetric ensemble of observers, having finite bare mass and trying to measure geometrical and physical properties of the environmental static (Schwarzschild) space-time. It is shown that, using the photon rockets (which the mass together with the mass of their fuel is also taken into account) they can managed to keep themselves on the fixed value of radius. The process of diminishing the total bare mass up to zero lasts infinitely long time. It is important that the problem is solved self-consistently, i.e., with full account for the back reaction of both bare mass and radiation from rockets on the space-time geometry.

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arXiv2010

Classical analog of quantum Schwarzschild black hole: local vs global, and the mystery of log(3)

The model is built in which the main global properties of classical and quasi-classical black holes become local. These are the event horizon, "no-hair", temperature and entropy. Our construction is based on the features of a quantum collapse, discovered when studying some quantum black hole models. But our model is purely classical, and this allows to use selfconsistently the Einstein equations and classical (local) thermodynamics and explain in this way the log(3)-puzzle.

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arXiv2010

On Classical Analogs of Quantum Schwarzschild and Reissner-Nordstrom Black Holes. Solving the "Mystery of log(3)"

The model is built in which the main global properties of classical and quasi-classical black holes become local. These are the event horizon, "no-hair", temperature and entropy. Our construction is based on the features of a quantum collapse, discovered while studying some quantum black hole models. But it is purely classical, and this allows to use the Einstein equations and classical (local) thermodynamics and explain in this way the "log(3)" - puzzle.

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arXiv2009

Brane Universe: Global Geometry

The global geometries of bulk vacuum space-times in the brane-universe models are investigated and classified in terms of geometrical invariants. The corresponding Carter-Penrose diagrams and embedding diagrams are constructed. It is shown that for a given energy-momentum induced on the brane there can be different types of global geometries depending on the signs of a bulk cosmological term and surface energy density of the brane (the sign of the latter does not influence the internal cosmological evolution). It is shown that in the Randall-Sundrum scenario it is possible to have an asymmetric hierarchy splitting even with a $Z_2$-symmetric matching of "our" brane to the bulk.

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arXiv2008

Quantum Black Holes. Black Hole Temperature without a Black Hole

The model is constructed, some features of which comes from quantum thin dust shells and is, in fact, an extension of the "no hair" property of classical black hole on a quantum level. It appears that the proposed classical analog of quantum black hole is heated, the temperature being exactly the Hawking's temperature.

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arXiv2005

Phantom shell around black hole and global geometry

We describe the possible scenarios for the evolution of a thin spherically symmetric self-gravitating phantom shell around the Schwarzschild black hole. The general equations describing the motion of the shell with a general form of equation of state are derived and analyzed. The different types of space-time R- and T-regions and shell motion are classified depending on the parameters of the problem. It is shown that in the case of a positive shell mass there exist three scenarios for the shell evolution with an infinite motion and two distinctive types of collapse. Analogous scenarios were classified for the case of a negative shell mass. In particular this classification shows that it is impossible for the physical observer to detect the fantom energy flow. We shortly discuss the importance of our results for astrophysical applications.

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arXiv2003

Black Hole Thermodynamics without a Black Hole?

In the present paper we consider, using our earlier results, the process of quantum gravitational collapse and argue that there exists the final quantum state when the collapse stops. This state, which can be called the ``no-memory state'', reminds the final ``no-hair state'' of the classical gravitational collapse. Translating the ``no-memory state'' into classical language we construct the classical analogue of quantum black hole and show that such a model has a topological temperature which equals exactly the Hawking's temperature. Assuming for the entropy the Bekenstein-Hawking value we develop the local thermodynamics for our model and show that the entropy is naturally quantized with the equidistant spectrum S + gamma_0*N. Our model allows, in principle, to calculate the value of gamma_0. In the simplest case, considered here, we obtain gamma_0 = ln(2).

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arXiv2000

Notes on a quantum gravitational collaps

Everybody knows what the classical black holes are. In short, this is a spacetime region beyond the so-called event horizon. The notion of the event horizon is mathematically well defined. The situation with a definition of quantum black hole is not so clear. The problem is that the classical event horizon can be defined only globally, i.e. in order to be sure we have a black hole we would need an infinite time interval. But, in classical physics we have trajectories off all the particles and equations of motion for all the fields and can, in principle, construct some ideal models for the gravitational collapse and study the black hole formation under different conditions.

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