arXiv subjects

S. V. Bolokhov

Publications and source records attributed to S. V. Bolokhov.

At least 37 records · Page 2Linked to original sources

arXiv2024

Late time decay of scalar and Dirac fields around an asymptotically de Sitter black hole in the Euler-Heisenberg electrodynamics

We compute the quasinormal modes of massive scalar and Dirac fields within the framework of asymptotically de Sitter black holes in Euler-Heisenberg non-linear electrodynamics. We pay particular attention to the regime $μM/m_{P}^2 \gg 1$, where $μ$ and $M$ denote the masses of the field and the black hole, respectively, and $m_{P}$ represents the Planck mass, covering a range from primordial to large astrophysical black holes. Through time-domain integration, we demonstrate that, contrary to the asymptotically flat case, the quasinormal modes also dictate the asymptotic decay of fields. Employing the 6th order WKB formula, we derive a precise analytic approximation for quasinormal modes in the regime $μM/m_{P}^2 \gg 1$ without resorting to expansion in terms of the inverse multipole number. This analytic expression takes on a concise form in the limit of linear electrodynamics, represented by the Reissner-Nordström black holes.

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arXiv2023

Black holes in Starobinsky-Bel-Robinson Gravity and the breakdown of quasinormal modes/null geodesics correspondence

We show that perturbations of a scalar field in the background of the black hole obtained with the Starobinsky-Bel-Robinson Gravity is unstable unless the dimensionless coupling $β$ describing the compactification of M-theory is small enough. In the sector of stability quasinormal spectrum show peculiar behavior both in the frequency and time domains: the ringing consists of two stages where two different modes dominate. The WKB method does not reproduce part of the spectrum including the fundamental mode, which is responsible for the first stage of the ringing. As a result, the correspondence between the high frequency quasinormal modes and characteristics of the null geodesics reproduces only one branch of the eikonal spectrum. The frequencies are obtained with the help of three methods (Frobenius, WKB and time-domain integration) with excellent agreement among them.

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arXiv2023

Long-lived quasinormal modes and overtones' behavior of the holonomy corrected black holes

Recently massless test scalar field perturbations of the holonomy corrected black holes [Z. Moreira et. al. Phys. Rev. D 107 (2023) 10, 104016] were studied in order to estimate quantum corrections to the quasinormal spectrum of a black hole. Here we study both the fundamental mode and overtones of scalar, electromagnetic and Dirac fields with the help of the Leaver method and higher order WKB formula with Padé approximants. We observe that the overtones depend on the geometry near the event horizon, while the fundamental mode is localized near the peak of the potential barrier, what agrees with previous studies. We showed that unlike a massless field, the massive one possesses arbitrarily long lived modes. We also obtain the analytical eikonal formula for quasinormal modes and its extension beyond eikonal approximation as a series in powers of $1/\ell$, where $\ell$ is the multipole number.

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arXiv2023

Fluxbrane polynomials and Melvin-like solutions for simple Lie algebras

This review dealt with generalized Melvin solutions for simple finite-dimensional Lie algebras. Each solution appears in a model which includes a metric and $n$ scalar fields coupled to $n$ Abelian 2-forms with dilatonic coupling vectors determined by simple Lie algebra of rank $n$. The set of $n$ moduli functions $H_s(z)$ comply with $n$ non-linear (ordinary) differential equations (of second order) with certain boundary conditions set. Earlier, it was hypothesized that these moduli functions should be polynomials in $z$ (so-called ``fluxbrane'' polynomials) depending upon certain parameters $p_s > 0$, $s = 1,\dots,n$. Here, we presented explicit relations for the polynomials corresponding to Lie algebras of ranks $n = 1,2,3,4,5$ and exceptional algebra $E_6$. Certain relations for the polynomials (e.g., symmetry and duality ones) were outlined. In a general case where polynomial conjecture holds, 2-form flux integrals are finite. The use of fluxbrane polynomials to dilatonic black hole solutions was also explored.

hep-th↗

arXiv2022

On fluxbrane polynomials for generalized Melvin-like solutions associated with rank 5 Lie algebras

We consider generalized Melvin-like solutions corresponding to Lie algebras of rank $5$ ($A_5$, $B_5$, $C_5$, $D_5$). The solutions take place in $D$-dimensional gravitational model with five Abelian 2-forms and five scalar fields. They are governed by five moduli functions $H_s(z)$ ($s = 1,...,5$) of squared radial coordinate $z=ρ^2$ which obey five differential master equations. The moduli functions are polynomials of powers $(n_1, n_2, n_3, n_4, n_5) = (5,8,9,8,5), (10,18,24,28,15), (9,16,21,24,25), (8,14,18,10,10)$ for Lie algebras $A_5$, $B_5$, $C_5$, $D_5$ respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued $5 \times 5$ matrix $ν$ connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in $A_5$ and $D_5$ cases) with the matrix representing a generator of the $\mathbb{Z}_2$-group of symmetry of the Dynkin diagram. The symmetry and duality identities for polynomials are obtained, as well as asymptotic relations for solutions at large distances.

hep-th↗

arXiv2022

Gravity assist as a test of relativistic gravity

We consider the gravity assist maneuver, that is, a correction of spacecraft motion at its passing near a planet, as a tool for evaluating the Eddington post-Newtonian parameters $β$ and $γ$, characterizing vacuum spherically symmetric gravitation fields in metric theories of gravity. We estimate the effect of variation in $β$ and $γ$ on a particular trajectory of a probe launched from the Earth's orbit and passing closely near Venus, where relativistic corrections slightly change the impact parameter of probe scattering in Venus's gravitational field. It is shown, in particular, that a change of $10^{-4}$ in $β$ or $γ$ leads to a shift of about 50 km in the probe's aphelion position.

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arXiv2022

On quasinormal modes in 4D black hole solutions in the model with anisotropic fluid

We consider a family of 4-dimensional black hole solutions from Dehnen et al. ( Grav. Cosmol. 9:153, arXiv: gr-qc/0211049, 2003) governed by natural number $q= 1, 2, 3 , \dots$, which appear in the model with anisotropic fluid and the equations of state: $p_r = -ρ(2q-1)^{-1}$, $p_t = - p_r$, where $p_r$ and $p_t$ are pressures in radial and transverse directions, respectively, and $ρ> 0$ is the density. These equations of state obey weak, strong and dominant energy conditions. For $q = 1$ the metric of the solution coincides with that of the Reissner-Nordström one. The global structure of solutions is outlined, giving rise to Carter-Penrose diagram of Reissner-Nordström or Schwarzschild types for odd $q = 2k + 1$ or even $q = 2k$, respectively. Certain physical parameters corresponding to BH solutions (gravitational mass, PPN parameters, Hawking temperature and entropy) are calculated. We obtain and analyse the quasinormal modes for a test massless scalar field in the eikonal approximation. For limiting case $q = + \infty$, they coincide with the well-known results for the Schwarzschild solution. We show that the Hod conjecture which connect the Hawking temperature and the damping rate is obeyed for all $q \geq 2$ and all (allowed) values of parameters.

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arXiv2021

Spherically symmetric space-times in generalized hybrid metric-Palatini gravity

We discuss vacuum static, spherically symmetric asymptotically flat solutions of the generalized hybrid metric-Palatini theory of gravity (generalized HMPG) suggested by Böhmer and Tamanini, involving both a metric $g_{μν}$ and an independent connection $\hat Γ_{μν}{}^α$; the gravitational field Lagrangian is an arbitrary function $f(R,P)$ of two Ricci scalars, $R$ obtained from $g_{μν}$ and $P$ obtained from $\hat Γ_{μν}{}^α$. The theory admits a scalar-tensor representation with two scalars $ϕ$ and $ξ$ and a potential $V(ϕ,ξ)$ whose form depends on $f(R,P)$. Solutions are obtained in the Einstein frame and transferred back to the original Jordan frame for a proper interpretation. In the completely studied case $V \equiv 0$, generic solutions contain naked singularities or describe traversable wormholes, and only some special cases represent black holes with extremal horizons. For $V(ϕ,ξ) \ne 0$, some examples of analytical solutions are obtained and shown to possess naked singularities. Even in the cases where the Einstein-frame metric $g^E_{μν}$ is found analytically, the scalar field equations need a numerical study, and if $g^E_{μν}$ contains a horizon, in the Jordan frame it turns to a singularity due to the corresponding conformal factor.

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arXiv2021

On generalized Melvin solutions for Lie algebras of rank 4

We deal with generalized Melvin-like solutions associated with Lie algebras of rank $4$ ($A_4$, $B_4$, $C_4$, $D_4$, $F_4$). Any solution has static cylindrically-symmetric metric in $D$ dimensions in presence of four Abelian 2-forms and four scalar fields. The solution is governed by four moduli functions $H_s(z)$ ($s = 1,...,4$) of squared radial coordinate $z=ρ^2$ obeying four differential equations of the Toda chain type. These functions are polynomials of powers $(n_1,n_2, n_3, n_4) = (4,6,6,4), (8,14,18,10), (7,12,15,16), (6,10,6,6), (22,42,30,16)$ for Lie algebras $A_4$, $B_4$, $C_4$, $D_4$, $F_4$, respectively. The asymptotic behaviour for the polynomials at large $z$ is governed by an integer-valued $4 \times 4$ matrix $ν$ connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in $A_4$ case) the matrix representing a generator of the $\mathbb{Z}_2$-group of symmetry of the Dynkin diagram. The symmetry properties and duality identities for polynomials are studied. We also present 2-form flux integrals over a $2$-dimensional submanifold. Dilatonic black hole analogs of the obtained Melvin-type solutions, e.g. "fantom" ones, are also considered. The phantom black holes are described by fluxbrane polynomials under consideration.

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arXiv2020

Matter accretion versus semiclassical bounce in Schwarzschild interior

We discuss the properties of the previously constructed model of a Schwarzschild black hole interior where the singularity is replaced by a regular bounce, ultimately leading to a white hole. The model is semiclassical in nature and uses as a source of gravity the effective stress-energy tensor (SET) corresponding to vacuum polarization of quantum fields, and a minimum spherical radius is a few orders of magnitude larger than the Planck length, so that the effects of quantum gravity should be still negligible. We estimate the other quantum contributions to the effective SET, caused by a nontrivial topology of spatial sections and particle production from vacuum due to a nonstationary gravitational field and show that these contributions are negligibly small as compared to the SET due to vacuum polarization. The same is shown for such classical phenomena as accretion of different kinds of matter to the black hole and its further motion to the would-be singularity. Thus, in a clear sense, our model of a semiclassical bounce instead of a Schwarzschild singularity is stable under both quantum and classical perturbations.

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arXiv2020

Hybrid metric-Palatini gravity: Regular stringlike configurations

We discuss static, cylindrically symmetric vacuum solutions of hybrid metric-Palatini gravity (HMPG), a recently proposed theory that has been shown to successfully pass the local observational tests and to produce a certain progress in cosmology. We use HMPG in its well-known scalar-tensor representation. The latter coincides with general relativity containing, as a source of gravity, a conformally coupled scalar field $ϕ$ and a self-interaction potential $V(ϕ)$. The $ϕ$ field can be canonical or phantom, and accordingly the theory splits into canonical and phantom sectors. We seek solitonic (stringlike) vacuum solutions of HMPG, that is, completely regular solutions with Minkowski metric far from the symmetry axis, with a possible angular deficit. A transition of the theory to the Einstein conformal frame is used as a tool, and many of the results apply to the general Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories as well as $f(R)$ theories of gravity. One of these results is a one-to-one correspondence between stringlike solutions in the Einstein and Jordan frames if the conformal factor that connects them is everywhere regular. An algorithm for construction of stringlike solutions in HMPG and scalar-tensor theories is suggested, and some examples of such solutions are obtained and discussed.

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arXiv2020

Hybrid metric-Palatini gravity: black holes, wormholes, singularities and instabilities

The hybrid metric-Palatini theory of gravity (HMPG), proposed in 2012 by T. Harko et al., is known to successfully describe both local (solar-system) and cosmological observations. We discuss static, spherically symmetric vacuum solutions of HMPG with the aid of its scalar-tensor representation. This scalar-tensor theory coincides with general relativity with a conformally coupled scalar field (which can be canonical or phantom), therefore the known solutions of this theory are re-interpreted in terms of HMPG. In particular, in the case of zero scalar field potential $V (ϕ)$, such that both Riemannian and Palatini Ricci scalars are zero, generic asymptotically flat solutions either contain naked singularities or describe traversable wormholes, and there are only special cases of black hole solutions with extremal horizons. There is also a one-parameter family of solutions with an infinite number of extremal horizons between static regions. Examples of analytical solutions with nonzero potentials $V (ϕ)$ are also described, among them black hole solutions with simple horizons which are generic but, for canonical scalars, they require (at least partly) negative potentials. With phantom scalars there are ``black universe'' solutions that lead beyond the horizon to an expanding universe instead of a singularity. Most of the solutions under consideration turn out to be unstable under scalar monopole perturbations, but some special black hole solutions are stable.

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arXiv2019

A possible semiclassical bounce instead of a Schwarzschild singularity

We have previously shown that the singularity in a Schwarzschild black hole of stellar or larger mass may be avoided in a semiclassical manner by using as a source of gravity the stress-energy tensor (SET) corresponding to vacuum polarization of quantum fields, with a minimum spherical radius a few orders of magnitude larger than the Planck length. In this note we estimate the nonlocal contribution to the total SET due to particle creation from vacuum. We show that this contribution is negligibly small as compared to vacuum polarization and does not affect the previously suggested scenario.

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arXiv2019

Rotating cylinders with anisotropic fluids in general relativity

We consider anisotropic fluids with directional pressures $p_i = w_i ρ$ ($ρ$ is the density, $w_i = $const, $i = 1,2,3$) as sources of gravity in stationary cylindrically symmetric space-times. We describe a general way of obtaining exact solutions with such sources, where the main features are splitting of the Ricci tensor into static and rotational parts and using the harmonic radial coordinate. Depending on the values of $w_i$, it appears possible to obtain general or special solutions to the Einstein equations, thus recovering some known solutions and finding new ones. Three particular examples of exact solutions are briefly described: with a stiff isotropic perfect fluid ($p = ρ$), with a distribution of cosmic strings of azimuthal direction (i.e., forming circles around the $z$ axis), and with a stationary combination of two opposite radiation flows along the $z$ axis.

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arXiv2019

Cylindrical wormholes: a search for viable phantom-free models in GR

The well-known problem of wormholes in general relativity (GR) is the necessity of exotic matter, violating the Weak Energy Condition (WEC), for their support. This problem looks easier if, instead of island-like configurations, one considers string-like ones, among them, cylindrically symmetric space-times with rotation. However, for cylindrical wormhole solutions a problem is the lacking asymptotic flatness, making it impossible to observe their entrances as local objects in our Universe. It was suggested to solve this problem by joining a wormhole solution to flat asymptotic regions at some surfaces $Σ_-$ and $Σ_+$ on different sides of the throat. The configuration then consists of three regions, the internal one containing a throat and two flat external ones. We discuss different kinds of source matter suitable for describing the internal regions of such models (scalar fields, isotropic and anisotropic fluids) and present two examples where the internal matter itself and the surface matter on both junction surfaces $Σ_\pm$ respect the WEC. In one of these models the internal source is a stiff perfect fluid whose pressure is equal to its energy density, in the other it is a special kind of anisotropic fluid. Both models are free from closed timelike curves. We thus obtain examples of regular twice asymptotically flat wormhole models in GR without exotic matter and without causality violations.

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arXiv2018

On generalized Melvin solutions for Lie algebras of rank 3

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 $H_1(z),H_2(z),H_3(z)$ ($z = ρ^2$ and $ρ$ is a radial variable), obeying three differential equations with certain boundary conditions imposed. These functions are polynomials with powers $(n_1,n_2, n_3) = (3,4,3), (6,10,6), (5,8,9)$ for Lie algebras $A_3$, $B_3$, $C_3$, respectively. The solutions depend upon integration constants $q_1, q_2, q_3 \neq 0$. The power-law asymptotic relations for polynomials at large $z$ are governed by integer-valued $3 \times 3$ matrix $ν$, which coincides with twice the inverse Cartan matrix $2 A^{-1}$ for Lie algebras $B_3$ and $C_3$, while in the $A_3$ case $ν= A^{-1} (I + P)$, where $I$ is the identity matrix and $P$ is a permutation matrix, corresponding to a generator of the $\mathbb{Z}_2$-group of symmetry of the Dynkin diagram. The duality identities for polynomials and asymptotic relations for solutions at large distances are obtained. 2-form flux integrals over a $2$-dimensional disc of radius $R$ and corresponding Wilson loop factors over a circle of radius $R$ are presented.

hep-th↗

arXiv2018

The Schwarzschild singularity: a semiclassical bounce?

We discuss the opportunity that the singularity inside a Schwarzschild black hole could be replaced by a regular bounce, described as a regular minimum of the spherical radius (instead of zero) and a regular maximum of the longitudinal scale (instead of infinity) in the corresponding Kantowski-Sachs metric. Such a metric in a vicinity of the bounce is shown to be a solution to the Einstein equations with the stress-energy tensor representing vacuum polarization of quantum matter fields, described by a combination of curvature-quadratic terms in the effective action. The indefinite parameters of the model can be chosen in such a way that it remains a few orders of magnitude apart from the Planck scale (say, on the GUT scale), that is, in a semiclassical regime.

gr-qc↗

arXiv2018

On cosmology in nonlinear multidimensional gravity with multiple factor spaces

Within the scope of multidimensional Kaluza--Klein gravity with nonlinear curvature terms and two spherical extra spaces of dimensions $m$ and $n$, we study the properties of an effective action for the scale factors of the extra dimensions. Dimensional reduction leads to an effective 4D multiscalar-tensor theory. Based on qualitative estimates of the Casimir energy contribution on a physically reasonable length scale, we demonstrate the existence of such sets of initial parameters of the theory in the case $m=n$ that provide a minimum of the effective potential that yield a fine-tuned value of the effective 4D cosmological constant. The corresponding size of extra dimensions depends of which conformal frame is interpreted as the observational one: it is about three orders of magnitude larger than the standard Planck length if we adhere to the Einstein frame, but it is $n$-dependent in the Jordan frame, and its invisibility requirement restricts the total dimension to values $D = 4+2n \leq 20$.

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