arXiv subjects

Andrei Zelnikov

Publications and source records attributed to Andrei Zelnikov.

At least 37 records · Page 2Linked to original sources

arXiv2018

The gravitational field of static p-branes in linearized ghost-free gravity

We study the gravitational field of static p-branes in D-dimensional Minkowski space in the framework of linearized ghost-free (GF) gravity. The concrete models of GF gravity we consider are parametrized by the non-local form factors $\exp(-\Box/μ^2)$ and $\exp(\Box^2/μ^4)$, where $μ^{-1}$ is the scale of non-locality. We show that the singular behavior of the gravitational field of p-branes in General Relativity is cured by short-range modifications introduced by the non-localities, and we derive exact expressions of the regularized gravitational fields, whose geometry can be written as a warped metric. For large distances compared to the scale of non-locality, $μr\rightarrow\infty$, our solutions approach those found in linearized General Relativity.

gr-qc↗

arXiv2017

On the Liouville 2D dilaton gravity models with sinh-Gordon matter

We study 1+1 dimensional dilaton gravity models which take into account backreaction of the sinh-Gordon matter field. We found a wide class of exact solutions which generalizes black hole solutions of the Jackiw-Teitelboim gravity model and its hyperbolic deformation.

hep-th↗

arXiv2017

Quantum radiation from an evaporating non-singular black hole

In this paper we study quantum radiation from an evaporating spherically symmetric non-singular black hole. We used a modified Hayward metric for a description of a non-singular black hole. We assume that the mass parameter of this metric depends on the advanced time, and choose this dependence so that it properly reproduces both black hole formation and its subsequent evaporation. We consider a quantum massless scalar field propagating in this geometry and use 2D approximation for the calculation of the quantum average of the stress-energy tensor. For the calculation of this quantity it is sufficient to find a map between the Killing times $u_+$ and $u_-$ at the future and past null infinities, established by the propagation of the radial null rays. In this formalism the quantum energy flux at the future null infinity can be expressed in terms of the function $u_+(u_-)$ and its derivatives. We developed a special formalism, which allows one to reduce the problem of the calculation of the quantum energy flux and other observables to a solution of a simple set of ordinary differential equations. We used this approach to study quantum effects in two cases: i) with the trivial, $α=1$ and ii) the non-trivial, $α\ne1$, redshift function. In both cases there exists an outburst of the quantum energy radiation from the inner domain of the black hole, close to the inner part of its apparent horizon. For $α=1$ this outburst is exponentially large. It is a direct consequence of the so-called mass inflation effect. We showed, that this severe problem can be solved by a proper choice of the redshift function. However, even in this case the emitted energy can be much larger than the initial mass of the evaporating black hole. This means that for a construction of a self-consistent model of a non-singular evaporating black hole the back-reaction effects are highly important.

hep-th↗

arXiv2017

Quantum radiation from a sandwich black hole

We discuss quantum radiation of a massless scalar field from a spherically symmetric nonsingular black hole with finite lifetime. Namely, we discuss a sandwich black-hole model, where a black hole is originally created by a collapse of a null shell of mass $M$, and later, after some time $ΔV$, it is disrupted by the collapse of the other shell with negative mass $-M$. We assume that between the shells the metric is static and either coincides with the Hayward metric or with a special generalization of it. We show that in both cases for sufficiently large parameter $ΔV$ the radiation after the formation of the black hole practically coincides with the Hawking result. We also calculated the radiation, emitted from the black hole interior. This radiation contains peak at the moment when the second shell intersects the inner horizon. In the standard sandwich metric (with the Hayward interior) this outburst of the energy is exponentially large. In the modified metric, which includes additional non-trivial redshift parameter, this exponent is suppressed. This is a result of significant decrease of the surface gravity of the inner horizon in the latter case. We discuss possible consequences of this result in context of the self-consistency requirement for nonsingular models with quantum radiation.

hep-th↗

arXiv2016

Head-on collision of ultrarelativistic particles in ghost-free theories of gravity

We study linearized equations of a ghost-free gravity in four- and higher-dimensional spacetimes. We consider versions of such a theory where the nonlocal modification of the $\Box$ operator has the form $\Box \exp[(-\Box/μ^2)^N]$, where $N=1$ or $N=2n$. We first obtain the Newtonian gravitational potential for a point mass for such models and demonstrate that it is finite and regular in any number of spatial dimensions $d\ge 3$. The second result of the paper is calculation of the gravitational field of an ultrarelativistic particle in such theories. And finally, we study a head-on collision of two ultrarelativistic particles. We formulated conditions of the apparent horizon formation and showed that there exists a mass gap for mini-black-hole production in the ghost-free theory of gravity. In the case when the center-of-mass energy is sufficient for the formation of the apparent horizon, the latter has two branches, the outer and the inner ones. When the energy increases the outer horizon tends to the Schwarzschild-Tangherlini limit, while the inner horizon becomes closer to $r=0$.

hep-th↗

arXiv2016

Radiation from an emitter in the ghost free scalar theory

We study radiation emitted by a time-dependent source of a scalar massless field in the framework of the ghost-free modifications of the theory. We consider a simple model of the emitter: namely,we assume that it is point-like and monochromatic. We focused on the most common versions of the ghost-free theory, where the propagator $\Box^{-1}$ is modified as follows $\exp(-(\Box/μ^2)^N) \Box^{-1}$, where $μ$ is the characteristic mass-scale of such $GF_N$-theory. We demonstrated that far from the source, in the wave-zone, the radiation asymptotically converges to its "classical" value for any $N\ge 1$. However, in the near-zone the behavior of the field is quite different from the "classical" case. The difference of field amplitude for the ghost-free field and for the classical one has an oscillatory behavior in this domain. A number of oscillations increases with $N$. The amplitude of these oscillations remain finite for even $N$, while it infinitely grows with frequency for odd $N$. This behavior indicates that even in the classical domain $GF_N$ theories might have pathological behavior.

hep-th↗

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

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

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

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

Minimal surfaces and entanglement entropy in anti-de Sitter space

According to Ryu and Takayanagi, the entanglement entropy in conformal field theory (CFT) is related through the AdS/CFT correspondence to the area of a minimal surface in the bulk. We study this holographic geometrical method of calculating the entanglement entropy in the vacuum case of a CFT which is holographically dual to empty anti-de Sitter (AdS) spacetime. Namely, we investigate the minimal surfaces spanned on boundaries of spherical domains at infinity of hyperbolic space, which represents a time-slice of AdS spacetime. We consider a generic position of two spherical domains: two disjoint domains, overlapping domains, and touching domains. In all these cases we find the explicit expressions for the minimal surfaces and the renormalized expression for the area. We study also the embedding of the minimal surfaces into full AdS spacetime and we find that for a proper choice of the static Killing vector we can model a dynamical situation of "tearing" of the minimal surface when the domains on which it is spanned are moved away from each other.

hep-th↗

arXiv2014

Entanglement entropy of spherical domains in anti-de Sitter space

It was proposed by Ryu and Takayanagi that the entanglement entropy in conformal field theory (CFT) is related through the AdS/CFT correspondence to the area of a minimal surface in the bulk. We apply this holographic geometrical method of calculating the entanglement entropy to study the vacuum case of a CFT which is holographically dual to empty anti-de Sitter (AdS) spacetime. We present all possible minimal surfaces spanned on one or two spherical boundaries at AdS infinity. We give exact analytical expressions for the regularized areas of these surfaces and identify finite renormalized quantities. In the case of two disjoint boundaries the existence of two different phases of the entanglement entropy is confirmed. A trivial phase corresponds to two disconnected minimal surfaces, while the other one corresponds to a tube connecting the spherical boundaries. A transition between these phases is reminiscent of the finite temperature deconfinement transition in the CFT on the boundary. The exact analytical results are thus consistent with previous numerical and approximate computations. We also briefly discuss the character of a spacetime extension of the minimal surface spanned on two uniformly accelerated boundaries.

hep-th↗

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↗

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↗

arXiv2012

Classical self-energy and anomaly

We study the problem of self-energy of pointlike charges in higher dimensional static spacetimes. Their energy, as a functional of the spacetime metric, is invariant under a specific continuous transformation of the metric. We show that the procedure of regularization of this formally divergent functional breaks this symmetry and results in an anomalous contribution to the finite renormalized self-energy. We proposed a method of calculation of this anomaly and presented an explicit expressions for it in the case of a scalar charge in four and five-dimensional static spacetimes. This anomalous correction proves to be zero in even dimensions, but it does not vanish in odd-dimensional spacetimes.

hep-th↗

arXiv2012

Self-energy of a scalar charge near higher-dimensional black holes

We study the problem of self-energy of charges in higher dimensional static spacetimes. Application of regularization methods of quantum field theory to calculation of the classical self-energy of charges leads to model-independent results. The correction to the self-energy of a scalar charge due to the gravitational field of black holes of the higher dimensional Majumdar-Papapetrou spacetime is calculated exactly. It proves to be zero in even dimensions, but it acquires non-zero value in odd dimensional spacetimes. The origin of the self-energy correction in odd dimensions is similar to the origin the conformal anomalies in quantum field theory in even dimensional spacetimes.

hep-th↗

arXiv2012

Scalar and electromagnetic fields of static sources in higher dimensional Majumdar-Papapetrou spacetimes

We study scalar massless and electromagnetic fields from static sources in a static higher dimensional spacetime. Exact expressions for static Green's functions for such problems are obtained in the background of the Majumdar-Papapetrou solutions of the Einstein-Maxwell equations. Using this result we calculated the force between two scalar or electric charges in the presence of one or several extremely charged black holes in equilibrium in the higher dimensional spacetime.

hep-th↗