Search

We investigated the possibility of the homogeneous and isotropic cosmological solution in Weyl geometry, which differs from the Riemannian geometry by adding the so called Weyl vector. The Weyl gravity is obtained by constructing the gravitational Lagrangian both to be quadratic in curvatures and conformal invariant. It is found that such solution may exist provided there exists the direct interaction between the Weyl vector and the matter fields. Assuming the matter Lagrangian is that of the perfect fluid, we found how such an interaction can be implemented. Due to the existence of quadratic curvature terms and the direct interaction the perfect fluid particles may be created straight from the vacuum, and we found the expression for the rate of their production which appeared to be conformal invariant. In the case of creating the universe ``from nothing'' in the vacuum state, we investigated the problem, whether this vacuum may persist or not. It is shown that the vacuum may persist with respect to producing the non-dust matter (with positive pressure), but cannot resist to producing the dust particles. These particles, being non-interactive, may be considered as the candidates for dark matter., Comment: 18 pages

The homogeneous and isotropic cosmological model in the Weyl conformal geometry is considered. We showed that, despite the conformal invariance, the dust matter is allowed in such a universe. It is shown that the number of dust particles is not conserved, i. e., they are continuously produced. The general form of the law for their creation is found., Comment: 10 pages

Using the principle of least action, the motion equations for a singular hypersurface of arbitrary type in quadratic gravity are derived. Equations containing the "external pressure" and the "external flow" components of the surface energy-momentum tensor together with the Lichnerowicz conditions serve to find the hypersurface itself, while the remaining ones define arbitrary functions that arise due to the implicit presence of the delta function derivative. It turns out that neither double layers nor thin shells exist for the quadratic Gauss-Bonnet term. It is shown that there is no "external pressure" for null singular hypersurfaces. The Lichnerowicz conditions imply the continuity of the scalar curvature in the case of spherically symmetric null singular hypersurfaces. These hypersurfaces must be thin shells if the Lichnerowicz conditions are necessary. It is shown that for this particular case the Lichnerowicz conditions can be completely removed therefore a spherically symmetric null double layer exists. Spherically symmetric null singular hypersurfaces in conformal gravity are explored as application., Comment: 32 pages, to be submitted to IJMPD

The Israel equations for thin shells in General Relativity are derived directly from the least action principle. The method is elaborated for obtaining the equations for double layers in quadratic gravity from the least action principle., Comment: 6 pages

We derived the equations for the double layers in Quadratic Gravity, using solely the least action principle. The advantage of our approach is that, in the process of calculation, the $\delta'$-function does not appear at all, and the $\delta$-functions appear for a moment and are mutually canceled prior to integration. We revealed the peculiar structure of the obtained equations, namely, that the surface energy-momentum tensor of the matter fields (constituents of the thin shells) does not play a role in the determination of the trajectory of the double layer. Also, we suggested that the space-like double layers may provide us with the adequate description of the creation of the universe from the black hole singularity. The related topics, including the Gauss-Bonnet term and $F(R)$-theories, are shortly discussed., Comment: 15 pages, minor proofs, submitted to CQG

The formation of primordial black holes in the early universe in the Brans-Dicke scalar-tensor theory of gravity is investigated. Corrections to the threshold value of density perturbations are found. Above the threshold, the gravitational collapse occurs after the cosmological horizon crossing. The corrections depend in a certain way on the evolving scalar field. They affect the probability of primordial black holes formation, and can lead to their clustering at large scales if the scalar field is inhomogeneous. The formation of the clusters, in turn, increases the probability of black holes merge and the corresponding rate of gravitational wave bursts. The clusters can provide a significant contribution to the LIGO/Virgo gravitational wave events, if part of the observed events are associated with primordial black holes., Comment: 14 pages, 2 figures; Presented at the 17th Russian Gravitational Conference (RUSGRAV-17), Saint Petersburg, Russia; references added, misprints corrected

Starting with the idea to describe phenomenologically the particle creation in the strong gravitational fields, we introduced explicitly the particle number nonconservation (= creation law) into the action integral with the corresponding Lagrange multiplier. Following the fundamental result by Ya. B. Zel'dovich and A. A. Starobinsky (1977) we then postulated that the rate of particle creation is proportional to the square of Weyl tensor. Concerning the conformal invariance, yet another question arises: how the scalar field could know about the surgery made on the metric tensor (if such an invariance is the fundamental law of Nature and not just the mathematical exercise)? The only way is that the scalar field is itself the part of metric, namely, the conformal factor. We showed, that such an identification results in the natural appearance of the quartic self-interaction term in the scalar field Lagrangian, which is needed to make particle massive. And it is just quartic, because our space-time is four-dimensional., Comment: 4 pages, based on report at the 18th Lomonosov conference, Moscow State University, Russia, 2017

We have analyzed the transformation from initial coordinates $(v,r)$ of the Vaidya metric with light coordinate $v$ to the most physical diagonal coordinates $(t,r)$. An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate $v$. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric and cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates $(t,r)$ is insufficient to cover the entire range of initial coordinates $(v,r)$ outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either $g_{00}=0$ or $g_{00}=\infty$.). The energy-momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false firewalls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates $(\eta,y)$, in which the solution is obtained in explicit form, and there is no energy-momentum tensor divergence., Comment: 13 pages, 10 figures

The classical Vaidya metric is transformed to the special diagonal coordinates in the case of the linear mass function allowing rather easy treatment. We find the exact analytical expressions for metric functions in these diagonal coordinates. Using these coordinates, we elaborate the maximum analytic extension of the Vaidya metric with a linear growth of the black hole mass and construct the corresponding Carter-Penrose diagrams for different specific cases. The derived global geometry seemingly is valid also for a more general behavior of the black hole mass in the Vaidya metric., Comment: 15 pages, 9 updated figures

We describe the general structure of the spherically symmetric solutions in the Weyl conformal gravity. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions, consisting of two classes, is found. The first one contains the solutions with constant two-dimensional curvature scalar, and the representatives are the famous Robertson--Walker metrics. We called one of them the "gravitational bubbles", which is compact and with zero Weyl tensor. These "gravitational bubbles" are the pure vacuum curved space-times (without any material sources, including the cosmological constant), which are absolutely impossible in General Relativity. This phenomenon makes it easier to create the universe from "nothing". The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family, which can be conformally covered by the thee-parameter Mannheim--Kazanas solution. We describe the general structure of the energy-momentum tensor in the spherical conformal gravity and construct the vectorial equation that reveals clearly some features of non-vacuum solutions., Comment: 7 pages, Talk given at the 9th Alexander Friedmann International Seminar on Gravitation and Cosmology, June 21, 2015 - June 27, 2015, Saint Petersburg, Russia

The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson--Walker metrics. One of them we called the "gravitational bubbles", which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from "nothing". The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim--Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics \`a la Vaidya, and the electrovacuum space-time metrics., Comment: 20 pages, published version

Starting from Israel equations for the spherically symmetric thin shells we introduce the effective potential and show how it can be used in constructing, without further thorough investigation, the corresponding Carter-Penrose diagrams describing clearly the global geometry of the composite space-time manifolds. We demonstrate, how this new method works, by considering all possible configurations for the neutral thin dust shell immersed into different types of Reissner-Nordstr\"om electro-vacuum manifolds., Comment: 70 pages, 60 figures

It is elaborated the complete classification of the possible types of the spherically symmetric global geometries for two types of electrically charged shells: (1) The charged shell as a single source of the gravitational field, when internal space-time is flat, and external space-time is the Reissner--Nordstr\"om metric; (2) The neutralizing shell with an electric charge opposite to the charge of the internal source with the Reissner--Nordstr\"om metric and with the Schwarzschild metric outside the shell., Comment: 76 pages, 62 figures

In this paper we derived Hawking radiation as a tuneling of massless particles through a non-singular horizon in the s-wave approximation. The back reaction of emitted modes on the background black hole geometry is self-consistently taken into account. This is arXive copy of the paper published in the Russian journal "Gravitation and Cosmology" in 1999., Comment: This is arXiv submission of the paper published in the Russian journal Gravitation and Cosmology in 1999

In the case of crossing thin dust shells the momentum conservation law is found. For two crossing isotropic shells it coincides with the 't Hooft-Dray formula. The system of one isotropic and one time-like shell is considered. In this case we found a very simple formula which relate velocities of dust shell before and after crossing., Comment: 19 pages, 5 figures, to be published in "Gravitation and Cosmology"

We describe some specific quantum black hole model. It is pointed out that the origin of a black hole entropy is the very process of quantum gravitational collapse. The quantum black hole mass spectrum is extracted from the mass spectrum of the gravitating source. The classical analog of quantum black hole is constructed., Comment: 14 pages. Talk given at the Fifth Workshop on Quantum Field Theory under the Influence of External Conditions, Leipzig, 10-14 Sept., 2001

We demonstrate how the Einstein's equations for the $D$-dimensional spherical gravity can be written in the covariant vector-like form. These equations reveal easily the causal structure of curved spherically symmetric manifolds and may appear useful in investigation of different models of brane universes., Comment: LaTex file, no figures

We develop a method for constructing asymptotic solutions of finite-difference equations and implement it to a relativistic Schroedinger equation which describes motion of a selfgravitating spherically symmetric dust shell. Exact mass spectrum of black hole formed due to the collapse of the shell is determined from the analysis of asymptotic solutions of the equation., Comment: 16 pages, 1 figure

We consider a massive selfgravitating shell as a model for collapsing body and a null selfgravitating shell as a model for quanta of Hawking radiation. It is show that the mass-energy spectra for the body and the radiation do not match. The way out of this difficulty is to consider not only out-going radiation but also the ingoing one. It means that the structure of black hole is changing during its evaporation resulting in the Bekenstein-Mukhanov spectrum for large masses., Comment: 11 pages, 2 figures, submitted to Phys.Rev.Lett

The quantum black hole model with a self-gravitating spherically symmetric thin dust shell as a source is considered. The shell Hamiltonian constraint is written and the corresponding Schroedinger equation is obtained. This equation appeared to be a finite differences equation. Its solutions are required to be analytic functions on the relevant Riemannian surface. The method of finding discrete spectra is suggested based on the analytic properties of the solutions. The large black hole approximation is considered and the discrete spectra for bound states of quantum black holes and wormholes are found. They depend on two quantum numbers and are, in fact, quasi-continuous. The quantum black hole bound state depends not only on mass but also on additional quantum number, and black holes with the same mass have different quantum hairs. These hairs exhibit themselves at the Planckian distances near the black hole horizon. For the observer who can not measure the distances smaller than the Planckian length the black hole has the only parameter, its mass. The other, non-measurable parameter leads to existence of the black hole entropy., Comment: Talk given on the Second international conference ``Quantum field theory and gravitation'', July 28 -August 2, 1997, Tomsk, Russia

The geometrodynamics of the spherical gravity with a selfgravitating thin dust shell as a source is constructed. The shell Hamiltonian constraint is derived and the corresponding Schroedinger equation is obtained. This equation appeared to be a finite differences equation. Its solutions are required to be analytic functions on the relevant Riemannian surface. The method of finding discrete spectra is suggested based on the analytic properties of the solutions. The large black hole approximation is considered and the discrete spectra for bound states of quantum black holes and wormholes are found. They depend on two quantum numbers and are, in fact, quasicontinuous., Comment: Latex, 32 pages, 5 figs

The black hole model with a self-gravitating charged spherical symmetric dust thin shell as a source is considered. The Schroedinger-type equation for such a model is derived. This equation appeared to be a finite differences equation. A theory of such an equation is developed and general solution is found and investigated in details. The discrete spectrum of the bound state energy levels is obtained. All the eigenvalues appeared to be infinitely degenerate. The ground state wave functions are evaluated explicitly. The quantum black hole states are selected and investigated. It is shown that the obtained black hole mass spectrum is compatible with the existence of Hawking's radiation in the limit of low temperatures both for large and nearly extreme Reissner-Nordstrom black holes. The above mentioned infinite degeneracy of the mass (energy) eigenvalues may appeared helpful in resolving the well known information paradox in the black hole physics., Comment: LaTeX file