arXiv subjects

Valeri P. Frolov

Publications and source records attributed to Valeri P. Frolov.

At least 73 records · Page 4Linked to original sources

arXiv2015

Spherical collapse of small masses in the ghost-free gravity

We discuss some properties of recently proposed models of a ghost-free gravity. For this purpose we study solutions of linearized gravitational equations in the framework of such a theory. We mainly focus on the version of the ghost-free theory with the exponential modification $\exp(\Box/μ^2)\Box^{-1}$ of the free propagator. The following three problems are discussed: (i) Gravitational field of a point mass; (ii) Penrose limit of a point source boosted to the speed of light; and (iii) Spherical gravitational collapse of null fluid. For the first problem we demonstrate that it can be solved by using the method of heat kernels and obtain a solution in a spacetime with arbitrary number of dimensions. For the second problem we also find the corresponding gyraton-type solutions of the ghost-free gravitational equations for any number of dimensions. For the third problem we obtain solutions for the gravitational field for the collapse of both "thin" and "thick" spherical null shells. We demonstrate how the ghost-free modification of the gravitational equations regularize the solutions of the linearized Einstein equations and smooth out their singularities.

hep-th↗

arXiv2015

Mass-gap for black hole formation in higher derivative and ghost free gravity

We study a spherical gravitational collapse of a small mass in higher derivative and ghost free theories of gravity. By boosting a solution of linearized equations for a static point mass in such theories we obtain in the Penrose limit the gravitational field of an ultra-relativistic particle. Taking a superposition of such solutions we construct a metric of a collapsing null shell in the linearized higher derivative and ghost free gravity. The latter allows one to find the gravitational field of a thick null shell. By analysing these solutions we demonstrate that in a wide class of the higher dimensional theories of gravity as well as for the ghost free gravity there exists a mass gap for the mini black hole production. We also found conditions when the curvature invariants remain finite at $r=0$ for the collapse of the thick null shell.

hep-th↗

arXiv2015

Biconformal symmetry and static Maxwell fields near higher-dimensional black holes

We study an electric field created by a static electric charge near the higher dimensional Reissner-Nordstrom black hole. The relation between the static Green functions on the D-dimensional Reissner-Nordstrom background and on the (D+2)-dimensional homogeneous Bertotti-Robinson spacetime is found. Using the biconformal symmetry we obtained a simple integral representation for the static Maxwell Green functions in arbitrary dimensions. We show that in a four-dimensional spacetime the static Green function obtained by the biconformal method correctly reproduces known results. We also found a closed form for the exact static Green functions and vector potentials in the five-dimensional Reissner-Nordstrom spacetime.

hep-th↗

arXiv2014

"Hybrid" Black Holes

We discuss a solution of the Einstein equations, obtained by gluing the external Kerr metric and the internal Weyl metric, describing an axisymmetric static vacuum distorted black hole. These metrics are glued at the null surfaces representing their horizons. For this purpose we use the formalism of massive thin null shells. The corresponding solution is called a "hybrid" black hole. The massive null shell has an angular momentum which is the origin of the rotation of the external Kerr spacetime. At the same time, the shell distorts the geometry inside the horizon. The inner geometry of the "hybrid" black hole coincides with the geometry of the interior of a non-rotating Weyl-distorted black hole. Properties of the "hybrid" black holes are briefly discussed.

gr-qc↗

arXiv2014

Bi-conformal symmetry and static Green functions in the higher-dimensional Reissner-Nordstrom spacetimes

We study a static scalar massless field created by a source located near an electrically charged higher dimensional spherically symmetric black hole. We demonstrated that there exist bi-conformal transformations relating static field solutions in the metric with different parameters of the mass M and charge Q. Using this symmetry we obtain the static scalar Green function in the higher dimensional Reissner-Nordstrom spacetimes.

hep-th↗

arXiv2014

Bi-conformal symmetry and static Green functions in the Schwarzschild-Tangherlini spacetimes

We study static massless minimally coupled scalar field created by a source in a static D-dimensional spacetime. We demonstrate that the corresponding equation for this field is invariant under a special transformation of the background metric. This transformation consists of the static conformal transformation of the spatial part of the metric accompanied by a properly chosen transformation of the red-shift factor. Both transformations are determined by one function of the spatial coordinates. We show that in a case of higher dimensional spherically symmetric black holes one can find such a bi-conformal transformation that the symmetry of the D-dimensional metric is enhanced after its application. Namely, the metric becomes a direct sum of the metric on a unit sphere and the metric of 2D anti-de Sitter space. The method of the heat kernels is used to find the Green function in this new space, that allows one, after dimensional reduction, to obtain a static Green function in the original space of the static black hole. The general useful representation of static Green functions is obtained in the Schwarzschild-Tangherlini spacetimes of arbitrary dimension. The exact explicit expressions for the static Green functions are obtained in such metrics for D < 6. It is shown that in the four dimensional case the corresponding Green function coincides with the Copson solution.

hep-th↗

arXiv2014

Do Black Holes Exist?

We discuss and compare definitions of a black hole based on the existence of event and apparent horizons. In this connection we present a non-singular model of a black hole with a closed apparent horizon and discuss its properties. We propose a massive thin shell model for consistent description of particles creation in black holes. Using this model we demonstrate that for black holes with mass much larger than the Planckian one the backreaction of the domain, where the particles are created, on the black hole parameters is negligibly small.

hep-th↗

arXiv2014

Charged particles in higher dimensional homogeneous gravitational field: Self-energy and self-force

A problem of self-energy and self-force for a charged point-like particle in a higher dimensional homogeneous gravitational field is considered. We study two cases, when a particle has usual electric charge and a case when it has a scalar charge, which is a source of a scalar massless minimally coupled field. We assume that a particle is at rest in the gravitational field, so that its motion is not geodesic and it has an acceleration a directed from the horizon. The self-energy of a point charge is divergent and the strength of the divergence grows with the number of dimensions. In order to obtain a finite contribution to the self- energy we use a covariant regularization method which is a modification of the proper time cut-off and other covariant regularizations. We analyze a relation between the self-energy and self-force and obtain explicit expressions for the self-forces for the electric and scalar charge in the spacetimes with the number of dimensions up to eight. General expressions for the case of higher dimensions are also obtained. We discuss special logarithmic factors ln(a), which are present both in the self-energy and self-force in odd dimensions. Finally, we compare the obtained results with the earlier known results both for the homogeneous gravitational field and for particles near black holes.

hep-th↗

arXiv2014

Rigidly rotating ZAMO surfaces in the Kerr spacetime

A stationary observer in the Kerr spacetime has zero angular momentum if his/her angular velocity $ω$ has a particular value, which depends on the position of the observer. Worldlines of such zero angular momentum observers (ZAMOs) with the same value of the angular velocity $ω$ form a three dimensional surface, which has the property that the Killing vectors generating time translation and rotation are tangent to it. We call such a surface a rigidly rotating ZAMO surface. This definition allows a natural generalization to the surfaces inside the black hole, where ZAMO's trajectories formally become spacelike. A general property of such a surface is that there exist linear combinations of the Killing vectors with constant coefficients which make them orthogonal on it. In this paper we discuss properties of the rigidly rotating ZAMO surfaces both outside and inside the black hole and relevance of these objects to a couple of interesting physical problems.

gr-qc↗

arXiv2014

Spectral line broadening in magnetized black holes

We consider weakly magnetized non-rotating black holes. In the presence of a regular magnetic field the motion of charged particles in the vicinity of a black hole is modified. As a result, the position of the innermost stable circular orbit (ISCO) becomes closer to the horizon. When the Lorentz force is repulsive (directed from the black hole) the ISCO radius can reach the gravitational radius. In the process of accretion charged particles (ions) of the accreting matter can be accumulated near their ISCO, while neutral particles fall down to the black hole after they reach $6M$ radius. The sharp spectral line Fe K$α$, emitted by iron ions at such orbits, is broadened when the emission is registered by a distant observer. In this paper we study this broadening effect and discuss how one can extract information concerning the strength of the magnetic field from the observed spectrum.

gr-qc↗

arXiv2014

Radiation from an emitter revolving around a magnetized non-rotating black hole

One of the methods of study of black holes in astrophysics is based on broadening of the spectrum of radiation of ionized Iron atoms. The line K$α$ associated with Iron emission at 6.4 keV is very narrow. If such an ion is revolving around a black hole, this line is effectively broadened as a result of the Doppler and gravitational redshift effects. The profile of the broaden spectrum contains information about the gravitational field of the black hole. In the presence of a regular magnetic field in the vicinity of a black holes the characteristics of the motion of charged ions are modified. In particular, their innermost stable circular orbits become closer to the horizon. The purpose of this work is to study how this effect modifies the spectrum broadening of lines emitted by such an ion. Our final goal is to analyze whether the change of the spectrum profiles can give us information about the magnetic field in the black hole vicinity.

gr-qc↗

arXiv2014

Information loss problem and a `black hole' model with a closed apparent horizon

In a classical description the spacetime curvature inside a black hole infinitely grows. In the domain where it reaches the Planckian value and exceeds it the Einstein equations should be modified. In the absence of reliable theory of quantum gravity it is instructive to consider simplified models. We assume that a spacetime curvature is limited by some value (of the order of the Planckian one). We use modified Vaidya metric, proposed by Hayward, to describe the black hole evaporation process. In such a spacetime the curvature near $r=0$ remains finite, it does not have an event horizon and its apparent horizon is closed. If the initial mass of such a `black hole' is much larger than the Planckian one its properties (as seen by an external observer) are practically the same as properties of the `standard' black hole with the event horizon. We study outgoing null rays in the vicinity of the outer apparent and introduce a notion of quasi-horizon. We demonstrate that particles, trapped inside a `black hole' during the evaporation process, finally may return to external space after the evaporation is completed. We also demonstrate that such quanta would have very large blue-shift. The absence of the event horizon makes it possible restoration of the unitarity in evaporating black holes.

hep-th↗

arXiv2013

Generalized Fermat's principle and action for light rays in a curved spacetime

We start with formulation of the generalized Fermat's principle for light propagation in a curved spacetime. We apply Pontryagin's minimum principle of the optimal control theory and obtain an effective Hamiltonian for null geodesics in a curved spacetime. We explicitly demonstrate that dynamical equations for this Hamiltonian correctly reproduce null geodesic equations. Other forms of the action for light rays in a curved spacetime are also discussed.

gr-qc↗

arXiv2013

Self-energy anomaly of an electric pointlike dipole in three-dimensional static spacetimes

We calculate the self-energy anomaly of a pointlike electric dipole located in a static $(2+1)$-dimensional curved spacetime. The energy functional for this problem is invariant under an infinite-dimensional (gauge) group of transformations parameterized by one scalar function of two variables. We demonstrate that the problem of the calculation of the self-energy anomaly for a pointlike dipole can be reduced to the calculation of quantum fluctuations of an effective two-dimensional Euclidean quantum field theory. We reduced the problem in question to the calculation of the conformal anomaly of an effective scalar field in two dimensions and obtained an explicit expression for the self-energy anomaly of an electric dipole in an asymptotically flat, regular $(2+1)$-dimensional spacetime which may have electrically neutral black-hole-like metrics with regular Killing horizon.

gr-qc↗

arXiv2013

Critical escape velocity for a charged particle moving around a weakly magnetized Schwarzschild black hole

We discuss charged particles motion in a spacetime of a weakly magnetized static non-rotating black hole. We study under which conditions a charged particle originally revolving around the black hole at a circular orbit after being kicked by another particle or photon can escape to infinity. We determine the escape velocity for particles at the innermost stable circular orbits and discuss the properties of particles moving with near-critical velocity. We show that in a general case such a motion is chaotic.

gr-qc↗

arXiv2012

Electron in higher-dimensional weakly charged rotating black hole spacetimes

We demonstrate separability of the Dirac equation in weakly charged rotating black hole spacetimes in all dimensions. The electromagnetic field of the black hole is described by a test field approximation, with vector potential proportional to the primary Killing vector field. It is shown that the demonstrated separability can be intrinsically characterized by the existence of a complete set of mutually commuting first order symmetry operators generated from the principal Killing-Yano tensor. The presented results generalize the results on integrability of charged particle motion and separability of charged scalar field studied in [1].

gr-qc↗

arXiv2012

Black holes, hidden symmetry and complete integrability: Brief Review

This paper contains a brief review of the remarkable properties of higher dimensional rotating black holes with the spherical topology of the horizon. We demonstrate that these properties are connected with and generated by a special geometrical object, the Principal Conformal Killing-Yano tensor (PCKYT). The most general solution, describing such black holes, Kerr-NUT-ADS metric, admits this structure. Moreover a solution of the Einstein Equations with (or without) a cosmological constant which possesses PCKYT is the Kerr-NUT-ADS metric. This object (PCKYT) is responsible for such remarkable properties of higher dimensional rotating black holes as: (i) complete integrability of geodesic equations and (ii) complete separation of variables of the important field equations.

gr-qc↗

arXiv2012

Anomaly and the self-energy of electric charges

We study the self energy of a charged particle located in a static D-dimensional gravitational field. We show that the energy functional for this problem is invariant under an infinite dimensional (gauge) group of transformations parameterized by one scalar function of (D-1)-variables. We demonstrate that the problem of the calculation of the self energy for a pointlike charge is equivalent to the calculation of the fluctuations $<ψ^2>$ for an effective (D-1)-dimensional Euclidean quantum field theory. Using point-splitting regularization we obtain an expression for the self energy and show, that it possesses anomalies. Explicit calculation of the self energy and its anomaly is done for the higher dimensional Majumdar-Papapetrou spacetimes.

hep-th↗