In this talk we address two important issues which could affect reaching the exponential and Kasner asymptotes in Einstein-Gauss-Bonnet cosmologies -- spatial curvature and anisotropy in

both three- and extra-dimensional subspaces. In the first part we consider cosmological evolution of spaces being the product of two isotropic and spatially curved subspaces. We consider all possible

number of...

We investigate the Universe evolution at late-time stages in models of teleparallel gravity with power-law nonminimal coupling and a decreasing power-law potential of the scalar field $\phi$. New asymptotic solutions are found analytically for these models in vacuum and with a perfect fluid. Applying numerical integration, we show that the cosmological evolution leads to these solutions for...

The meaning of the wave function of the Universe was actively discussed in 1980s. In most works on quantum cosmology it is accepted that the wave function defines the probability amplitude for the Universe to have some space geometry, or to be found in some point of the Wheeler superspace. It seems that the wave function gives maximally objective description compatible with quantum theory....

f(R) gravity with higher derivatives are represented in terms of the chiral cosmological models. Symmetries of a chiral space of obtained models are studied. Examples of exact solutions are found and diccassed.

We consider cosmological perturbations in the theory of gravity with nonminimal kinetic coupling. The Lagrangian of the theory contains the term $\zeta G^{ij}\phi_{,i}\phi_{,j}$, and represents the particular example of a general Horndeski Lagrangian, which results in second-order field equations. We derive a complete set of equations for scalar and tensor pertubations. The scalar and tensor...

The idea of a cosmological attractor is based on the observation that in many models the kinetic term in Jordan frame practically does not affect the slow-roll parameters during inflation. In the case of many scalar fields, the use of this observation gets a possibility to construct a one-field inflationary model that approximates the original multifield model. In the talk, the examples of...

The graviton-to-photon conversion effect in a magnetized relativistic lepton plasma is considered. This effect can be important for the possible generation of electromagnetic radiation accompanying coalescence of relativistic compact neutron star -- black hole binaries. The relativistic electron-positron plasma can be generated near the surface of a rotating magnetized neutron star (a radio...

In the framework of Multiple Point Principle (MPP), where the existence of the two degenerate vacua of the Universe: the first, ElectroWeak vacuum with $\approx 246$ GeV ("true vacuum"), and the second at Planck scale $\sim 10^{18}$ GeV ("false vacuum"); we investigated the gravitational black-hole-hedgehog's solution with magnetic field contribution in the GraviWeak unification model...

The cosmological dynamics of a non-locally corrected gravity theory, involving a power of the inverse d'Alembertian, is investigated. Casting the dynamical equations into local form, the fixed points of the models are derived, as well as corresponding de Sitter and power-law solutions. Necessary and sufficient conditions on the model parameters for the existence of de Sitter solutions are...

Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or stationary configurations. This is due to the objective complexity of solving the Einstein equations under the assumption of nonstationarity. We present an...

We consider spherically symmetric black holes with minimally coupled scalar fields and concentrate our attention on asymptotically flat self-gravitating configurations having the event horizons located at radii much smaller than 2M. We think of such configurations as rigorous mathematical models of the gravitating objects, surrounded by dark matter, at the centres of normal galaxies. In...

All known solutions to the Einstein equations describing rotating cylindrical wormholes lack asymptotic flatness and therefore cannot describe wormhole entrances as local objects in our Universe.To overcome this difficulty, wormhole solutions are joined to flat asymptotic regions at some surfaces $\Sigma_-$ and $\Sigma_+$. The whole configuration thus consists of three regions, the internal...

Victor Berezin, Vyacheslav Dokuchaev and Yuri Eroshenko

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Institute for Nuclear Research of the Russian Academy of Sciences
Moscow, Russia
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The role of the exact solutions in gravitational theories is impossible to overestimate. But the intrinsically

nonlinear character of gravitational eauations makes solving them a very...

The study of vacuum polarization effects in strong gravitational fields is a pertinent issue since such effects may play a role in the cosmological scenario and the construction of a self-consistent model of black hole evaporation. These effects can be taken into account by solving the semiclassical backreaction equations

$ G^{\mu}*{\nu}=8 \pi \langle T^{\mu}*{\nu} \rangle, \qquad...

Now, after decades of purely theoretical research, a new era begins in the study of black holes. Thanks to such projects as the Event Horizon Telescope, LIGO and VIRGO, eLISA and others, it will be possible to obtain observational data and to test various theoretical models. Therefore, it is important to close some gaps

in the theories of black holes that have not been resolved in due time....

We consider a multidimensional Kaluza–-Klein-like model with nonlinear curvature terms and two spherical extra spaces of dimensions $m$ and $n$. The properties of an effective action for the scale factors of extra dimensions are studied. Dimensional reduction leads to an effective 4D multiscalar-tensor theory. Based on qualitative estimates of the Casimir energy contribution at a physically...

There are two main processes during inflation - quick space expansion and grows of the field energy due to fluctuations. In simplest and most widespread realization of the inflationary scenario, only one dimensional parameter plays essential role - the Hubble parameter $H$.

If a compact space is involved into consideration, another dimensional parameter - an extra space size $l$ -...

Theories with broken Lorentz invariance have attracted much attention recently. For example, a promising approach to quantization of gravity based on abandoning Lorentz invariance has been proposed by Horava. At low energies Horava gravity reduces to a special case of the so-called Einstein-aether theory - a widely studied phenomenological model, where Lorentz violation is described by a...

Generalized Melvin solutions for rank-$3$ Lie algebras $A_3$, $B_3$ and $C_3$

are considered. Any solution contains metric, three Abelian 2-forms and

three scalar fields. It is governed by three moduli functions $H_1(z),H_2(z),H_3(z)$

($z = \rho^2$ and $\rho$ is a radial variable), obeying

three differential equations with certain boundary conditions

imposed. These functions are...

We study the loop effects on the geometry and boundary conditions of time-dependent black hole spacetimes and analyze the energy measured

by an infalling observer near their horizons. As a result of our studies (A.J. Nurmagambetov & I.Y. Park JHEP05(2018)167) we obtain a trans-

Planckian energy in the time-dependent case, the importance of which for the black hole (in)formation is discussed.

We study $D$-dimensional Einstein-Gauss-Bonnet gravitational model including the Gauss-Bonnet term and the cosmological term $\Lambda$. We find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters $H >0$ and $h$, corresponding to factor spaces of dimensions $m >2$ and $l > 2$, respectively. These solutions contain

a fine-tuned...

Disk accretion is a very common phenomenon in the Universe: planets are born in accretion disks near young stars, bright X-ray outbursts of accretion disks occur in close star binary systems, supermassive black holes accrete matter from the surrounding disks. Observation behavior of accretion disks in different sources are described in the terms of standard accretion disk model (Shakura &...