arXiv subjects

Dmitri V. Fursaev

Publications and source records attributed to Dmitri V. Fursaev.

At least 19 recordsLinked to original sources

arXiv2025

Memories of Gravitational Shockwaves

Gravitational shockwaves produce perturbations of field systems. We study classical scalar and electromagnetic fields and gravitational memory effects left after the action on the fields of plane-fronted gravitational shockwaves. The gravitational memory plays a key role for the choice of Cauchy data which determine the perturbations. We demonstrate that field systems`remember' only a spatial `profile' of the shock, but not the form of the signal. Moreover the dependence on the spatial profile can be expressed in a geometric way as a transformation of fields under coordinate supertranslations defined near the shockwave front. We also discuss applications of our results to astrophysics.

gr-qc↗

arXiv2022

Black Hole Thermodynamics and Perturbative Quantum Gravity

An introduction to generalized thermodynamics of quantum black holes, in the one-loop approximation, is given. The material is aimed at graduate students. The topics include: quantum evaporation of black holes, Euclidean formulation of quantum theory on black hole backgrounds, the Hartle-Hawking-Israel state, generalized entropy of a quantum black hole and its relation to the entropy of entanglement.

gr-qc↗

arXiv2020

Massless Cosmic Strings in Spacetimes with Global Parabolic Isometries

A class of curved spacetimes with global parabolic isometries (GPI) is introduced. These isometries have fixed point sets on two-dimensional null surfaces which can be interpreted as worldsheets of massless cosmic strings. Back reaction effects of the strings in such spacetimes can be described exactly, in terms of a nontrivial holonomy at the worldsheet. We show that the GPI spacetimes are type $N$ geometries of the Petrov classification. We describe a number of features of these spacetimes, including properties of Killing horizons associated to GPI. As an example, we consider a circular massless cosmic string in the de Sitter universe and present the metric in new coordinates centered at the string worldsheet.

gr-qc↗

arXiv2018

Massless Cosmic Strings in Expanding Universe

Circular massless cosmic strings which move with the speed of light in the de Sitter universe are described. Construction of the background geometry is based on parabolic isometries of the de Sitter spacetime. Microscopic circular cosmic strings may appear at the Planck epoch and then grow up to the Hubble size. We analyze: images of the strings, influence of strings on trajectories of matter, formation of overdensities, and shifts of energies of photons. These effects allow one to discriminate massless strings from their massive cousins. The present work extends our results on straight massless cosmic strings in Minkowsky spacetime to curved backgrounds.

gr-qc↗

arXiv2016

Anomalies, entropy and boundaries

A relation between the conformal anomaly and the logarithmic term in the entanglement entropy is known to exist for CFT's 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 non-trivial integrated anomaly if an odd-dimensional spacetime has boundaries. We show that, similarly, there exists a logarithmic term in the entanglement entropy when the entangling surface crosses the boundary of spacetime. The relation of the entanglement entropy to the integrated conformal anomaly is elaborated for three-dimensional theories. Distributional properties of intrinsic and extrinsic geometries of the boundary in the presence of conical singularities in the bulk are established. This allows one to find contributions to the entropy that depend on the relative angle between the boundary and the entangling surface.

hep-th↗

arXiv2013

Distributional Geometry of Squashed Cones

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 $Σ$ so that the surface is allowed to have extrinsic curvatures. A new feature of the squashed conical singularities is that the surface terms in the integral invariants, in the limit of small angle deficit, now depend also on the extrinsic curvatures of $Σ$. A case of invariants which are quadratic polynomials of the Riemann curvature is elaborated in different dimensions and applied to several problems related to entanglement entropy. The results are in complete agreement with computations of the logarithmic terms in entanglement entropy of 4D conformal theories [2]. Among other applications of the suggested method are logarithmic terms in entanglement entropy of non-conformal theories and a holographic formula for entanglement entropy in theories with gravity duals.

hep-th↗

arXiv2012

Entanglement Renyi Entropies in Conformal Field Theories and Holography

An entanglement Renyi entropy for a spatial partition of a system is studied in conformal theories which admit a dual description in terms of an anti-de Sitter gravity. The divergent part of the Renyi entropy is computed in 4D conformal N=4 super Yang-Mills theory at a weak coupling. This result is used to suggest a holographic formula which reproduces the Renyi entropy at least in the leading approximation. The holographic Renyi entropy is an invariant functional set on a codimension 2 minimal hypersurface in the bulk geometry. The bulk space does not depend on order $n$ of the Renyi entropy. The holographic Renyi entropy is a sum of local and non-local functionals multiplied by polynomials of $1/n$.

hep-th↗

arXiv2010

`Thermodynamics' of Minimal Surfaces and Entropic Origin of Gravity

Deformations of minimal surfaces lying in constant time slices in static space-times are studied. An exact and universal formula for a change of the area of a minimal surface under shifts of nearby point-like particles is found. It allows one to introduce a local temperature on the surface and represent variations of its area in a thermodynamical form by assuming that the entropy in the Planck units equals the quarter of the area. These results provide a strong support to a recent hypothesis that gravity has an entropic origin, the minimal surfaces being a sort of holographic screens. The gravitational entropy also acquires a definite physical meaning related to quantum entanglement of fundamental degrees of freedom across the screen.

hep-th↗

arXiv2007

Entanglement Entropy in Quantum Gravity and the Plateau Problem

In a quantum gravity theory the entropy of entanglement $S$ between the fundamental degrees of freedom spatially divided by a surface is discussed. The classical gravity is considered as an emergent phenomenon and arguments are presented that: 1) $S$ is a macroscopical quantity which can be determined without knowing a real microscopical content of the fundamental theory; 2) $S$ is given by the Bekenstein-Hawking formula in terms of the area of a co-dimension 2 hypesurface $\cal B$; 3) in static space-times $\cal B$ can be defined as a minimal hypersurface of a least volume separating the system in a constant time slice. It is shown that properties of $S$ are in agreement with basic properties of the von Neumann entropy. Explicit variational formulae for $S$ in different physical examples are considered.

hep-th↗

arXiv2006

Proof of the Holographic Formula for Entanglement Entropy

Entanglement entropy for a spatial partition of a quantum system is studied in theories which admit a dual description in terms of the anti-de Sitter (AdS) gravity one dimension higher. A general proof of the holographic formula which relates the entropy to the area of a codimension 2 minimal hypersurface embedded in the bulk AdS space is given. The entanglement entropy is determined by a partition function which is defined as a path integral over Riemannian AdS geometries with non-trivial boundary conditions. The topology of the Riemannian spaces puts restrictions on the choice of the minimal hypersurface for a given boundary conditions. The entanglement entropy is also considered in Randall-Sundrum braneworld models where its asymptotic expansion is derived when the curvature radius of the brane is much larger than the AdS radius. Special attention is payed to the geometrical structure of anomalous terms in the entropy in four dimensions. Modification of the holographic formula by the higher curvature terms in the bulk is briefly discussed.

hep-th↗

arXiv2006

Entanglement Entropy in Critical Phenomena and Analogue Models of Quantum Gravity

A general geometrical structure of the entanglement entropy for spatial partition of a relativistic QFT system is established by using methods of the effective gravity action and the spectral geometry. A special attention is payed to the subleading terms in the entropy in different dimensions and to behaviour in different states. It is conjectured, on the base of relation between the entropy and the action, that in a fundamental theory the ground state entanglement entropy per unit area equals $1/(4G_N)$, where $G_N$ is the Newton constant in the low-energy gravity sector of the theory. The conjecture opens a new avenue in analogue gravity models. For instance, in higher dimensional condensed matter systems, which near a critical point are described by relativistic QFT's, the entanglement entropy density defines an effective gravitational coupling. By studying the properties of this constant one can get new insights in quantum gravity phenomena, such as the universality of the low-energy physics, the renormalization group behavior of $G_N$, the statistical meaning of the Bekenstein-Hawking entropy.

hep-th↗

arXiv2004

Interaction of higher-dimensional rotating black holes with branes

We study interaction of rotating higher dimensional black holes with a brane in space-times with large extra dimensions. We demonstrate that in a general case a rotating black hole attached to a brane can loose bulk components of its angular momenta. A stationary black hole can have only those components of the angular momenta which are connected with Killing vectors generating transformations preserving a position of the brane. In a final stationary state the null Killing vector generating the black hole horizon is tangent to the brane. We discuss first the interaction of a cosmic string and a domain wall with the 4D Kerr black hole. We then prove the general result for slowly rotating higher dimensional black holes interacting with branes. The characteristic time when a rotating black hole with the gravitational radius $r_0$ reaches this final stationary state is $T\sim r_0^{p-1}/(Gσ)$, where $G$ is the higher dimensional gravitational coupling constant, $σ$ is the brane tension, and $p$ is the number of extra dimensions.

gr-qc↗

arXiv2004

Rotating black holes in brane worlds

We study interaction of rotating higher dimensional black holes with a brane in space-times with large extra dimensions. We demonstrate that a rotating black hole attached to a brane can be stationary only if the null Killing vector generating the black hole horizon is tangent to the brane world-sheet. The characteristic time when a rotating black hole with the gravitational radius $r_0$ reaches this final stationary state is $T\sim r_0^{p-1}/(Gσ)$, where $G$ is the higher dimensional gravitational coupling constant, $σ$ is the brane tension, and $p$ is the number of extra dimensions.

gr-qc↗

arXiv2004

Can One Understand Black Hole Entropy without Knowing Much about Quantum Gravity?

It is a common belief now that the explanation of the microscopic origin of the Bekenstein-Hawking entropy of black holes should be available in quantum gravity theory, whatever this theory will finally look like. Calculations of the entropy of certain black holes in string theory do support this point of view. In the last few years there also appeared a hope that an understanding of black hole entropy may be possible even without knowing the details of quantum gravity. The thermodynamics of black holes is a low energy phenomenon, so only a few general features of the fundamental theory may be really important. The aim of this review is to describe some of the proposals in this direction and the results obtained.

gr-qc↗

arXiv2003

Spectral Geometry of Operator Polynomials and Applications to QFT

A class of non-linear eigenvalue problems defined in the form of operator polynomials is investigated. The problems are related to wave equations which appear in a relativistic quantum field theory. Spectral asymptotics for this class are found explicitly. The properties of operator polynomials are analyzed for scalar, spinor and gauge fields. It is also shown how to use these results in finite temperature theories.

hep-th↗

arXiv1998

A Note on Entanglement Entropy and Conformal Field Theory

It is pointed out that the entanglement entropy of quantum fields near the horizon of a two-dimensional black hole can be derived by means of the conformal field theory. This can be done in a way analogous to the computation of the entropy of BTZ black holes. The important feature of the considered case is that the degrees of freedom of the conformal theory are states localized in the physical space-time.

hep-th↗

arXiv1997

Finite Temperature Effective Potential for Gauge Models in de Sitter Space

The one-loop effective potential for gauge models in static de Sitter space at finite temperatures is computed by means of the $ζ$--function method. We found a simple relation which links the effective potentials of gauge and scalar fields at all temperatures. In the de Sitter invariant and zero-temperature states the potential for the scalar electrodynamics is explicitly obtained, and its properties in these two vacua are compared. In this theory the two states are shown to behave similarly in the regimes of very large and very small radii a of the background space. For the gauge symmetry broken in the flat limit ($a \to \infty$) there is a critical value of a for which the symmetry is restored in both quantum states. Moreover, the phase transitions which occur at large or at small a are of the first or of the second order, respectively, regardless the vacuum considered. The analytical and numerical analysis of the critical parameters of the above theory is performed. We also established a class of models for which the kind of phase transition occurring depends on the choice of the vacuum.

hep-th↗

arXiv1996

Heat-kernel Coefficients and Spectra of the Vector Laplacians on Spherical Domains with Conical Singularities

The spherical domains $S^d_β$ with conical singularities are a convenient arena for studying the properties of tensor Laplacians on arbitrary manifolds with such a kind of singular points. In this paper the vector Laplacian on $S^d_β$ is considered and its spectrum is calculated exactly for any dimension $d$. This enables one to find the Schwinger-DeWitt coefficients of this operator by using the residues of the $ζ$-function. In particular, the second coefficient, defining the conformal anomaly, is explicitly calculated on $S^d_β$ and its generalization to arbitrary manifolds is found. As an application of this result, the standard renormalization of the one-loop effective action of gauge fields is demonstrated to be sufficient to remove the ultraviolet divergences up to the first order in the conical deficit angle.

hep-th↗