# Sergey N. SolodukhinUniversity of Tours | UFR · Département de Physique

Sergey N. Solodukhin

Professor (Full)

## About

125

Publications

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## Publications

Publications (125)

The entanglement entropy is a fundamental quantity which characterizes the
correlations between sub-systems in a larger quantum-mechanical system. For two
sub-systems separated by a surface the entanglement entropy is proportional to
the area of the surface and depends on the UV cutoff which regulates the
short-distance correlations. The geometrica...

We analyze the Ricci flow of a non-compact metric that describes a two-dimensional black hole. We consider entanglement entropy of a 2d black hole which is due to the quantum correlations between two subsystems: one is inside and the other is outside the black hole horizon. It is demonstrated that the entanglement entropy is monotonic along the Ric...

We discuss a class of (local and non-local) theories of gravity that share
same properties: i) they admit the Einstein spacetime with arbitrary
cosmological constant as a solution; ii) the on-shell action of such a theory
vanishes and iii) any (cosmological or black hole) horizon in the Einstein
spacetime with a positive cosmological constant does...

Inspired by Son's model for graphene, we consider a $(2+1)$-dimensional fermionic system in which fermions are described by four-component spinors. These fermions are proposed to interact with an electromagnetic field originating from a four-dimensional setting, as the graphene plate is embedded in 4d Minkowski spacetime. In this framework, a chira...

In this note we focus on the backreaction effects due to the chiral anomaly. The chiral anomaly gives rise to certain modifications in the conserved currents. In the case of the Maxwell gauge fields there appears a new contribution to the electric current proportional to the background magnetic field. This phenomenon is known as the chiral magnetic...

The classical black hole spacetime is modified semiclassically, depending strongly on the choice of the quantum states. In particular, for the Boulware state the spacetime often takes a wormhole structure mimicking closely a spacetime with a horizon. In this paper, in the context of the two-dimensional dilaton Russo-Susskind-Thorlacius model, we co...

The classical black hole spacetime is modified semiclassically, depending strongly on the choice of the quantum states. In particular, for the Boulware state the spacetime often takes a wormhole structure mimicking closely a spacetime with a horizon. In this paper, in the context of the two-dimensional dilaton RST model, we consider all possible im...

In the presence of boundaries, the quantum anomalies acquire additional boundary terms. In odd dimensions, the integrated conformal anomaly, for which the bulk contribution is known to be absent, is nontrivial due to the boundary terms. These terms became a subject of active study in the recent years. In the present paper, we continue our previous...

In the presence of boundaries, the quantum anomalies acquire additional boundary terms. In odd dimensions the integrated conformal anomaly, for which the bulk contribution is known to be absent, is non-trivial due to the boundary terms. These terms became a subject of active study in the recent years. In the present paper we continue our previous s...

A hybrid quantum state is a combination of the Hartle-Hawking state for the physical particles and the Boulware state for the nonphysical ones (such as ghosts), as was introduced in our earlier work [Y. Potaux et al., Phys. Rev. D 105, 025015 (2022).]. We present a two-dimensional example, based on the Russo-Susskind-Thorlacius model, when the corr...

A hybrid quantum state is a combination of the Hartle-Hawking state for the physical particles and the Boulware state for the non-physical ones (such as ghosts), as was introduced in our earlier work [1]. We present a two-dimensional example, based on the RST model, when the corresponding back-reacted spacetime is a causal diamond, geodesically com...

Within the Russo-Susskind-Thorlacius (RST) two-dimensional model that includes a scalar (dilaton) field we address the important question of how the classical black hole geometry is modified in a semiclassical gravitational theory. It is the principle goal of this paper to analyze what is the back-reacted geometry that corresponds to a given quantu...

Within the Russo-Susskind-Thorlacius (RST) two-dimensional model that includes a scalar (dilaton) field we address the important question of how the classical black hole geometry is modified in a semiclassical gravitational theory. It is the principle goal of this paper to analyze what is the back-reacted geometry that corresponds to a given quantu...

In odd dimensions the integrated conformal anomaly is entirely due to the boundary terms [1]. In this paper we present a detailed analysis of the anomaly in five dimensions. We give the complete list of the boundary conformal invariants that exist in five dimensions. Additionally to 8 invariants known before we find a new conformal invariant that c...

In odd dimensions the integrated conformal anomaly is entirely due to the boundary terms \cite{Solodukhin:2015eca}. In this paper we present a detailed analysis of the anomaly in five dimensions. We give the complete list of the boundary conformal invariants that exist in five dimensions. Additionally to 8 invariants known before we find a new conf...

In the framework of dimensional regularization, we propose a generalization of the renormalization group equations in the case of the perturbative quantum gravity that involves renormalization of the metric and of the higher order Riemann curvature couplings. The case of zero cosmological constant is considered. Solving the renormalization group (R...

In the framework of dimensional regularization, we propose a generalization of the renormalization group equations in the case of the perturbative quantum gravity that involves renormalization of the metric and of the higher order Riemann curvature couplings. The case of zero cosmological constant is considered. Solving the renormalization group (R...

The Bekenstein-Hawking (BH) entropy is expected to be modified by certain correction terms in the quantum loop expansion. As is well known the logarithmic terms in the entropy of black holes appear as a one-loop addition to the classical BH entropy. In this note we study the further modifications of the logarithmic terms in the entropy of the Schwa...

We study a free scalar field ϕ in a fixed curved background spacetime subject to a higher derivative field equation of the form F(□)ϕ=0, where F is a polynomial of the form F(□)=∏i(□−mi2) and all masses mi are distinct and real. Using an auxiliary field method to simplify the calculations, we obtain expressions for the Belinfante-Rosenfeld symmetri...

The Bekenstein-Hawking (BH) entropy is expected to be modified by certain correction terms in the quantum loop expansion. As is well known the logarithmic terms in the entropy of black holes appear as a one-loop addition to the classical BH entropy. In this note we study the further modifications of the logarithmic terms in the entropy of the Schwa...

We study a free scalar field $\phi$ in a fixed curved background spacetime subject to a higher derivative field equation of the form $F(\Box)\phi =0$, where $F$ is a polynomial of the form $F(\Box)= \prod_i (\Box-m_i^2)$ and all masses $m_i$ are distinct and real. Using an auxiliary field method to simplify the calculations, we obtain expressions f...

The presence of a horizon is the principal marker for black holes as they appear in the classical theory of gravity. In General Relativity (GR), horizons have several defining properties. First, there exists a static spherically symmetric solution to vacuum Einstein equations which possesses a horizon defined as a null-surface on which the time-lik...

The radiation emitted by horizonless exotic compact objects (ECOs), such as wormholes, 2-2-holes, fuzzballs, gravastars, boson stars, collapsed polymers, superspinars etc., is expected to be strongly suppressed when compared to the radiation of black holes. If large primordial curvature fluctuations collapse into such objects instead of black holes...

The presence of a horizon is the principal marker for black holes as they appear in the classical theory of gravity. In General Relativity (GR), horizons have several defining properties. First, there exists a static spherically symmetric solution to vacuum Einstein equations which possesses a horizon defined as a null-surface on which the time-lik...

When a spacetime has boundaries, the entangling surface does not have to be necessarily compact and it may have boundaries as well. Then there appear a new, boundary, contribution to the entanglement entropy due to the intersection of the entangling surface with the boundary of the spacetime. We study the boundary contribution to the logarithmic te...

In the presence of boundaries the integrated conformal anomaly is modified by the boundary terms so that the anomaly is non-vanishing in any (even or odd) dimension. The boundary terms are due to extrinsic curvature whose exact structure in $d=3$ and $d=4$ has recently been identified. In this note we present a holographic calculation of those term...

We present a number of explicit calculations of Renyi and entanglement entropies in situations where the entangling surface intersects the boundary in $d$-dimensional Minkowski spacetime. When the boundary is a single plane we compute the contribution to the entropy due to this intersection, first in the case of the Neumann and Dirichlet boundary c...

A relation between the conformal anomaly and the logarithmic term in the entanglement entropy is known to exist for CFTs in even dimensions. In odd dimensions, the local anomaly and the logarithmic term in the entropy are absent. As was observed recently, there exists a nontrivial integrated anomaly if an odd-dimensional spacetime has boundaries. W...

We analyze the structure of the boundary terms in the conformal anomaly
integrated over a manifold with boundaries. We suggest that the anomalies of
type B, polynomial in the Weyl tensor, are accompanied with the respective
boundary terms of the Gibbons-Hawking type. Their form is dictated by the
requirement that they produce a variation which comp...

I formulate several statements demonstrating that the local metric
redefinition can be used to reduce the UV divergences present in the quantum
action for the Einstein gravity in $d=4$ dimensions. In its most general form,
the proposal is that any UV divergences in the quantum action can be removed by
an appropriate field re-definition and a renorm...

We formulate certain inequalities for the geometric quantities characterizing
causal diamonds in curved and Minkowski spacetimes. These inequalities involve
the red-shift factor which, as we show explicitly in the spherically symmetric
case, is monotonic in the radial direction and it takes its maximal value at
the centre. As a byproduct of our dis...

We analyze the Wald entropy for different forms of the conformal anomaly in
six dimensions. In particular we focus on the anomaly which arises in a
holographic calculation of Henningson and Skenderis. The various presentations
of the anomaly differ by some total derivative terms. We calculate the
corresponding Wald entropy for surfaces which do not...

We discuss the renormalization of the Newton constant due to fields of
various spin $s$. We first briefly review the cases of $s=0, \, 1/2, \, 1,\,
3/2$ already discussed in the literature and notice the appearance of the
well-known contact terms for the vector bosons. We then extend this discussion
of the contact terms to massive vector fields, $p...

where is the trace part and is the traceless part of , and , . In (1) we deliberately did not include the terms with extrinsic curvature as we want to study closely the case of [12]. The entangling surface Σ is at in metric (1). Applying the replica trick (for a review on this method see [15]) we change the periodicity of τ to be from 0 to , where...

The total derivatives in the gravitational action are usually disregarded as
non-producing any non-trivial dynamics. In the context of the gravitational
entropy, within Wald's approach, these terms are considered irrelevant as
non-contributing to the entropy. On the other hand, the total derivatives are
usually present in the trace anomaly in dimen...

For a given quantum field theory, provided the area of the entangling surface
is fixed, what surface maximizes entanglement entropy? We analyze the answer to
this question in four and higher dimensions. Surprisingly, in four dimensions
the answer is related to a mathematical problem of finding surfaces which
minimize the Willmore (bending) energy a...

In this note we demonstrate that, as we conjectured earlier in [1], the
a-charge in the conformal anomaly in dimension $d=2n$ manifests in a $n$-point
correlation function of energy momentum tensor of a CFT considered in flat
spacetime with a conical defect. We consider in detail dimensions $d=2,\, 4,\,
6$ and give a general formula for arbitrary $...

We explore the new technique developed recently in \cite{Rosenhaus:2014woa}
and suggest a correspondence between the $N$-point correlation functions on
spacetime with conical defects and the $(N+1)$-point correlation functions in
regular Minkowski spacetime. This correspondence suggests a new systematic way
to evaluate the correlation functions on...

A regularization procedure developed in [1] for the integral curvature
invariants on manifolds with conical singularities is generalized to the case
of squashed cones. In general, the squashed conical singularities do not have
rotational O(2) symmetry in a subspace orthogonal to a singular surface
$\Sigma$ so that the surface is allowed to have ext...

The a-theorem is demonstrated for the RG flows of entanglement entropy in two
and four dimensions. In four dimensions we relate it to the term quadratic in
intrinsic derivative of the dilaton along the entangling surface in the dilaton
entropy. The a-theorem, similarly to the c-theorem in two dimensions, then
follows from the positivity of the 2-po...

We analyze the dependence of the effective action and the entanglement
entropy in the Maxwell theory on the gauge fixing parameter $a$ in $d$
dimensions. For a generic value of $a$ the corresponding vector operator is
nonminimal. The operator can be diagonalized in terms of the transverse and
longitudinal modes. Using this factorization we obtain a...

The linearized massive gravity in three dimensions, over any maximally
symmetric background, is known to be presented in a self-dual form as a first
order equation which encodes not only the massive Klein-Gordon type field
equation but also the supplementary transverse-traceless conditions. We
generalize this construction to higher dimensions. The...

We consider the situation when a globally defined four-dimensional field
system is separated on two entangled sub-systems by a dynamical (random)
two-dimensional surface. The reduced density matrix averaged over ensemble of
random surfaces of fixed area and the corresponding average entropy are
introduced. The average entanglement entropy is analyz...

We calculate parameters in the low energy gravitational effective action and the entanglement entropy in a wide class of theories characterized by improved ultraviolet (UV) behavior. These include (i) local and non-local Lorentz invariant theories in which inverse propagator is modified by higher-derivative terms and (ii) theories described by non-...

We propose that the logarithmic term in the entanglement entropy computed in a conformal field theory for a (d−2)-dimensional round sphere in Minkowski spacetime is identical to the logarithmic term in the entanglement entropy of extreme black hole. The near horizon geometry of the latter is H2×Sd−2. For a scalar field this proposal is checked by d...

Reformulating our recent result (arXiv:1007.1246 [hep-th]) in coordinate space we point out that no matter how regular is
short-distance behavior of Green’s function the entanglement entropy in the corresponding quantum field theory is always UV
divergent. In particular, we discuss a recent example by Padmanabhan (arXiv:1007.5066 [gr-qc]) of a regu...

We calculate entanglement entropy in a non-relativistic field theory described by the Schr\"odinger operator. We demonstrate that the entropy is characterized by i) the area law and ii) UV divergences that are identical to those in the relativistic field theory. These observations are further supported by a holographic consideration. We use the non...

An exact spherically symmetric black hole solution of a recently proposed noncommutative gravity theory based on star products and twists is constructed. This is the first nontrivial exact solution of that theory. The resulting noncommutative black hole quite naturally exhibits holographic behavior; outside the horizon it has a fuzzy shell-like str...

In this note we prove that the volume of a causal diamond associated with an
inertial observer in asymptotically de Sitter 4-dimensional space-time is
monotonically increasing function of cosmological time. The asymptotic value of
the volume is that of in maximally symmetric de Sitter space-time. The
monotonic property of the volume is checked in t...

We study the black hole entropy as entanglement entropy and propose a resolution to the species puzzle. This resolution comes out naturally due to the fact that in the presence of $N$ species the universal gravitational cutoff is $\Lambda=M_{\rm Planck}/\sqrt{N}$, as opposed to $M_{\rm Planck}$. We demonstrate consistency of our solution by showing...

We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface Σ that separates two subsystems of quantum strongly coupled N=4SU(N) superconformal gauge theory. We extend this result and calculate entanglement entropy of a generic 4d conformal fi...

We determine the black hole quasi-normal mode spectrum for
tensor perturbations in topologically massive AdS-gravity. In the
special case of chiral gravity quasi-normal modes are absent despite
of the presence of a horizon. In the process we uncover a simple
algebraic structure in the quasi normal modes spectrum: the tower of
QNM's consists of desc...

In a previous paper we obtained formulae for the volume of a causal diamond or Alexandrov open set I+(p)∩I−(q) whose duration τ(p,q) is short compared with the curvature scale. In the present Letter we obtain asymptotic formulae valid when the point q recedes to the future boundary I+ of an asymptotically de Sitter space–time. The volume (at fixed...

In a previous paper we obtained formulae for the volume of a causal diamond or Alexandrov open set $I^+(p) \cap I^-(q)$ whose duration $\tau(p,q) $ is short compared with the curvature scale. In the present paper we obtain asymptotic formulae valid when the point $q$ recedes to the future boundary ${\cal I}^+$ of an asymptotically de-Sitter spaceti...

We study to what extent wormholes can mimic the observational features of black holes. It is surprisingly found that many features that could be thought of as ``characteristic'' of a black hole (endowed with an event horizon) can be closely mimicked by a globally static wormhole, having no event horizon. This is the case for: the apparently irrever...

The geometry of causal diamonds or Alexandrov open sets whose initial and final events $p$ and $q$ respectively have a proper-time separation $\tau$ small compared with the curvature scale is a universal. The corrections from flat space are given as a power series in $\tau$ whose coefficients involve the curvature at the centre of the diamond. We g...

A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter space is generalized to include entanglement entropy of black holes living on the boundary of anti-de Sitter space. The generalized proposal is verified in boundary dimensions d=2 and d=...

The holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk action which gauge invariance is only up to the boundary terms. We analyze in detail how the gravitational anomal...

The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-formulated in terms of the zwei...

Whether or not a system is unitary can be seen from the way it, if perturbed, relaxes back to equilibrium. The relaxation of a semiclassical black hole can be described in terms of a correlation function which exponentially decays with time. In the momentum space it is represented by an infinite set of complex poles to be identified with the quasin...

We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex...

Minkowski space is a physically important space-time for which the finding an adequate holographic description is an urgent problem. In this paper we develop further the proposal made in hep-th/0303006 for the description as a duality between Minkowski space-time and a Conformal Field Theory defined on the boundary of the light-cone. We focus on th...

We start by pointing out that certain Riemann surfaces appear rather naturally in the context of wave equations in the black hole background. For a given black hole there are two closely related surfaces. One is the Riemann surface of complexified ``tortoise'' coordinate. The other Riemann surface appears when the radial wave equation is interprete...

A conformal field theory (CFT) description of the near-horizon physics, the Rindler reflection amplitude and the Hawking radiation was presented. The conformal theory interpretations of the near-horizon phenomena were done in terms of one and two-point functions in the boundary Liouville theory. A notion of horizon state, which was analogous to the...

Minkowski space can be sliced, outside the light-cone, in terms of Euclidean anti-de Sitter and Lorentzian de Sitter slices. In this paper we investigate what happens when we apply holography to each slice separately. This yields a dual description living on two spheres, which can be interpreted as the boundary of the light-cone. The infinite numbe...

We study the propagating gravitational waves as a tool to probe the extra dimensions. In the set-up with one compact extra dimension and non-gravitational physics resigning on the 4-dimensional subspace (brane) of 5-dimensional spacetime we find the Green's function describing the propagation of 5-dimensional signal along the brane. The Green's fun...

Particles colliding at impact parameter much larger than the effective gravitational radius can not classically form a black hole and just scatter off the radial potential barrier separating the particles. We show that the process of the black hole production can still go quantum-mechanically via familiar mechanism of the under-barrier tunneling. T...

We study the process of relaxation back to thermal equilibrium in $(1+1)$-dimensional conformal field theory at finite temperature. When the size of the system is much larger than the inverse temperature, perturbations decay exponentially with time. On the other hand, when the inverse temperature is large, the relaxation is oscillatory with charact...

We obtain exact expressions for the quasinormal modes of various spin for the Ba\~nados-Teitelboim-Zanelli black hole. These modes determine the relaxation time of black hole perturbations. Exact agreement is found between the quasinormal frequencies and the location of the poles of the retarded correlation function of the corresponding perturbatio...

We suggest a simple model to study the problem of the black hole production in particle collisions. The cross-section for the classical and quantum production is analysed within this model. In particular, the possibility to form a black hole in collision of low energy particles (or at large impact parameter) via the quantum tunneling mechanism is p...

We study gravitational aspects of brane-world scenarios. We show that the bulk Einstein equations together with the junction condition imply that the induced metric on the brane satisfies the full nonlinear Einstein equations with a specific effective stress-energy tensor. This result holds for any value of the bulk cosmological constant. The analy...

A holographic correspondence between data on horizon and space-time physics is investigated. We find similarities with the AdS/CFT correspondence, based on the observation that the optical metric near the horizon describes a Euclidean asymptotically anti-de Sitter space. This picture emerges for a wide class of static space-times with a non-degener...

We find explicitly the induced graviton propagator on de Sitter branes embedded in various five-dimensional spacetimes; de Sitter branes in AdS and Minkowski space are particular cases. By studying the structure of the momentum-space propagator, we are able to extract interesting physics, much of which is qualitatively different from that of flat b...

We develop a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. This involves regularizing the bulk on-shell supergravity action in a covariant way, computing all divergences, adding counterterms to cancel them and then removing the regulator. We explicitly work out the case of pure gravity up to six d...

We study gravitational aspects of Brane-World scenarios. We show that the bulk Einstein equations together with the junction condition imply that the induced metric on the brane satisfies the full non-linear Einstein equations with a specific effective stress energy tensor. This result holds for any value of the bulk cosmological constant. The anal...

The entropy-to-energy bound is examined for a quantum scalar field confined to a cavity and satisfying Robin condition on the boundary of the cavity. It is found that near certain points in the space of the parameter defining the boundary condition the lowest eigenfrequency (while non-zero) becomes arbitrarily small. Estimating, according to Bekens...

We develop a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. This involves regularizing the bulk on-shell supergravity action in a covariant way, computing all divergences, adding counterterms to cancel them and then removing the regulator. We explicitly work out the case of pure gravity up to six d...

We obtain an Einstein metric of constant negative curvature given an arbitrary boundary metric in three dimensions, and a conformally flat one given an arbitrary conformally flat boundary metric in other dimensions. In order to compute the on-shell value of the gravitational action for these solutions, we propose to integrate the radial coordinate...

The recently proposed technique to regularize the divergences of the gravitational action on non-compact space by adding boundary counterterms is studied. We propose prescription for constructing the boundary counterterms which are polynomial in the boundary curvature. This prescription is efficient for both asymptotically Anti-de Sitter and asympt...

The existence of black hole horizon is considered as a boundary condition to be imposed on the fluctuating metrics. The coordinate invariant form of the condition for class of spherically symmetric metrics is formulated. The diffeomorphisms preserving this condition act in (arbitrary small) vicinity of the horizon and form the group of conformal tr...

A quantum field described by the field operator Δa = Δ + aδΣ involving a δ-like potential concentrated on a subspace Σ is considered. Mathematically, the treatment of the δ-potential is based on the theory of self-adjoint extension of the unperturbed operator Δ. We give the general expressions for the resolvent and the heat kernel of the perturbed...

The product space configuration AdS2xS2 (with l and r being radiuses of the components) carrying the electric charge Q is demonstrated to be an exact solution of the semiclassical Einstein equations in presence of the Maxwell field. If the logarithmic UV divergences are absent in the four-dimensional theory the solution we find is identical to the...

In the context of the bulk-boundary correspondence we study the correlation functions arising on a boundary for different types of boundary conditions. The most general condition is the mixed one, interpolating between the Neumann and Dirichlet conditions. We obtain the general expressions for the correlators on a boundary in terms of Green's funct...

Non-vacuum exact solutions in two-dimensional Poincaré gauge gravity are studied. Scalar matter fields are of particular interest, since they effectively describe the boson string models with non-trivial (Riemann--Cartan) two-dimensional dynamical geometry. We explicitly demonstrate, via an ansatz, that our recently suggested method of integration...

The one-loop quantum corrections to geometry and thermodynamics of black hole are studied for the two-dimensional RST model. We chose boundary conditions corresponding to the eternal black hole being in the thermal equilibrium with the Hawking radiation. The equations of motion are exactly integrated and we obtain the quantum-corrected metric (2.29...

The string-black-hole correspondence is considered in the context of the correspondence principle proposed recently by Horowitz and Polchinski. We demonstrate that the entropy of string states and the entropy of a Schwarzschild black hole can be matched including the subleading terms which depend on mass logarithmically. We argue the necessity to i...

A quantum field described by the field operator $\Delta_{a}=\Delta+ a\delta_\Sigma$ involving a $\delta$-like potential is considered. Mathematically, the treatment of the $\delta$-potential is based on the theory of self-adjoint extension of the unperturbed operator $\Delta$. We give the general expressions for the resolvent and the heat kernel of...

We consider the extremal limit of a black hole geometry of the Reissner-Nordstrom type and compute the quantum corrections to its entropy. Universally, the limiting geometry is the direct product of two 2-dimensional spaces and is characterized by just a few parameters. We argue that the quantum corrections to the entropy of such extremal black hol...

The string-black hole correspondence is considered in the context of the correspondence principle proposed recently by Horowitz and Polchinski. We demonstrate that the entropy of string states and the entropy of a Schwarzschild black hole can be matched including the subleading terms which depend on mass logarithmically. We argue the necessity to i...

Formulating the statistical mechanics for a scalar field with nonminimal ξRφ2 coupling in a black hole background we propose modification of the original 't Hooft “brick wall” prescription. Instead of the Dirichlet condition we suggest some scattering ansatz for the field functions at the horizon. This modifies the energy spectrum of the system and...

We discuss the connection between different entropies introduced for black hole. It is demonstrated on the two-dimensional example that the (quantum) thermodynamical entropy of a hole coincides (including UV-finite terms) with its statistical-mechanical entropy calculated according to 't Hooft and regularized by Pauli-Villars. Comment: 10 pages, la...

We consider the behaviour of a quantum scalar field on three-dimensional Euclidean backgrounds: Anti-de Sitter space, the regular BTZ black hole instanton and the BTZ instanton with a conical singularity at the horizon. The corresponding heat kernel and effective action are calculated explicitly for both rotating and non-rotating holes. The quantum...

Quantum corrections are studied for a charged black hole in a two-dimensional model obtained by spherisymmetric reduction of the 4D Einstein-Maxwell theory. The classical (tree-level) thermodynamics is re-formulated in the framework of the off-shell approach, considering systems at arbitrary temperature. This implies a conical singularity at the ho...

We discuss the statistical-mechanical entropy of black hole calculated according to 't Hooft. It is argued that in presence of horizon the statistical mechanics of quantum fields depends on their UV behavior. The ``brick wall'' model was shown to provide a correct description when the ``brick wall'' parameter is less than any UV cut-off.

We apply the method of conical singularities to calculate the tree-level entropy and its one-loop quantum corrections for a charged Kerr black hole. The Euclidean geometry for the Kerr-Newman metric is considered. We show that for an arbitrary periodization in Euclidean space there exists a conical singularity at the horizon. Its $\delta$-function...

The one-loop quantum corrections to the geometry and thermodynamics of a black hole are studied for the two-dimensional RST model. We choose boundary conditions corresponding to the eternal black hole being in thermal equilibrium with Hawking radiation. The equations of motion are exactly integrated. One of the solutions obtained is the constant cu...

One-loop divergences appearing in the entropy of a quantum black hole are proven to be completely eliminated by the standard renormalization of both the gravitational constant and other coefficients by the R(2)-terms in the effective gravitational action. The essential point of the proof is that due to the higher order curvature terms the entropy d...

According to Gibbons and Hawking a consistent variational procedure applied to the gravitational action requires a certain balance between the volume and boundary parts of the action. We consider the problem of preserving this balance in the quantum effective action for the matter non-minimally coupled to metric. It is shown that one has to add a s...