The Conical Singularity And Quantum Corrections To Entropy Of Black Hole

Abstract

For general finite temperature different from the Hawking one there appears a well known conical singularity in the Euclidean classical solution of gravitational equations. The method of regularizing the cone by regular surface is used to determine the curvature tensors for such a metrics. This allows one to calculate the one-loop matter effective action and the corresponding one-loop quantum corrections to the entropy in the framework of the path integral approach of Gibbons and Hawking. The two-dimensional and four-dimensional cases are considered. The entropy of the Rindler space is shown to be divergent logarithmically in two dimensions and quadratically in four dimensions that coincides with results obtained earlier. For the eternal 2D black hole we observe finite, dependent on the mass, correction to the entropy. The entropy of the 4D Schwarzschild black hole is shown to possess an additional (in comparison with the 4D Rindler space) logarithmically divergent correction which does not vanish in the limit of infinite mass of the black hole. We argue that infinities of the entropy in four dimensions are renormalized by the renormalization of the gravitational coupling.

JINR E2-94-246, Latex, 23 pages

References in corpus (17)

• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• On Geometric Entropy
• Black Hole Entropy in Canonical Quantum Gravity and Superstring Theory
• Dynamical Origin of the Entropy of a Black Hole
• Black hole thermodynamics and information loss in two dimensions
• A Comment on Entropy and Area
• The Heat Kernel Expansion on a Cone and Quantum Fields Near Cosmic Strings
• Remarks on geometric entropy
• Spectral Geometry and One-loop Divergences on Manifolds with Conical Singularities
• Wavefunction of a Black Hole and the Dynamical Origin of Entropy
• Black Hole Entropy in Two Dimensions
• Liouville Black Holes
• Evaporating Black Holes and Entropy
• Generalized Sums over Histories for Quantum Gravity I. Smooth Conifolds
• Generalized Sums over Histories for Quantum Gravity II. Simplicial Conifolds
• On Higher Derivative Gravity in Two Dimensions

Cited by in corpus (161)

• Aspects of Holographic Entanglement Entropy
• Holographic Entanglement Entropy: An Overview
• Entanglement entropy in free quantum field theory
• Entanglement entropy of black holes
• A Quantum Focussing Conjecture
• Entanglement entropy, conformal invariance and extrinsic geometry
• Black Hole Entropy and Entropy of Entanglement
• On the Description of the Riemannian Geometry in the Presence of Conical Defects
• Black Hole Entropy without Brick Walls
• Universal terms for the entanglement entropy in 2+1 dimensions
• Proof of the Quantum Null Energy Condition
• Remarks on the entanglement entropy for disconnected regions
• Holographic Entanglement Entropy in Lovelock Gravities
• Entanglement Entropy from a Holographic Viewpoint
• Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates
• AdS/CFT and Strong Subadditivity of Entanglement Entropy
• Proof of the Weak Gravity Conjecture from Black Hole Entropy
• Thermal Fields, Entropy, and Black Holes
• On one-loop renormalization of black-hole entropy
• Holography with Gravitational Chern-Simons Term
• Entanglement entropy for the n-sphere
• On "Non-Geometric" Contribution To The Entropy Of Black Hole Due To Quantum Corrections
• Entropy of Schwarzschild black hole and string-black hole correspondence
• Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions
• Conical geometry and quantum entropy of a charged Kerr black hole
• Quantum scalar field on three-dimensional (BTZ) black hole instanton: heat kernel, effective action and thermodynamics
• Simulating Magnetohydrodynamical Flow with Constrained Transport and Adaptive Mesh Refinement; Algorithms & Tests of the AstroBEAR Code
• Some Results on Mutual Information of Disjoint Regions in Higher Dimensions
• One-loop Renormalization of Black Hole Entropy Due to Non-minimally Coupled Matter
• On the Entropy of a Quantum Field in the Rotating Black Holes
• Thermal Fluctuations and Black Hole Entropy
• Universal Entanglement and Boundary Geometry in Conformal Field Theory
• Soft hairy horizons in three spacetime dimensions
• Higher derivative corrections to Kerr black hole thermodynamics
• On One-loop Quantum Corrections to the Thermodynamics of Charged Black Holes
• Entropy and temperature of black holes in a gravity's rainbow
• Entanglement entropy of black holes and AdS/CFT correspondence
• Cones, Spins and Heat Kernels
• Black hole entropy: statistical mechanics agrees thermodynamics
• Black Hole Entropy: Off-Shell vs On-Shell
• Echo of the Dark: gravitational waves from dark SU(3) Yang-Mills theory
• Entanglement entropy for a Dirac fermion in three dimensions: vertex contribution
• Black Hole Entropy in the O(N) Model
• Microscopic and Macroscopic Entropy of Extremal Black Holes in String Theory
• Algebraic approach to quantum black holes: logarithmic corrections to black hole entropy
• Numerical determination of the entanglement entropy for free fields in the cylinder
• Gravitational effective action and entanglement entropy in UV modified theories with and without Lorentz symmetry
• Generalized Second Law for Cosmology
• Anomalies, entropy and boundaries
• Logarithmic correction to black hole entropy from the nonlocality of quantum gravity
• Logarithmic correction to the Cardy-Verlinde formula in Achucarro-Oritz Black Hole
• Area law and vacuum reordering in harmonic networks
• Generalized free energy landscape of black hole phase transition
• Restoring Unitarity in BTZ Black Hole
• Non-polynomial Lagrangian approach to Regular Black Holes
• Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory
• Two-dimensional Quantum-Corrected Eternal Black Hole
• Renyi entropy, stationarity, and entanglement of the conformal scalar
• Heat-kernel Coefficients and Spectra of the Vector Laplacians on Spherical Domains with Conical Singularities
• Quantum entropy of the general non-extreme stationary axisymmetric black hole due to minimally coupled quantum scalar field
• Holographic screens in ultraviolet self-complete quantum gravity
• Divergences problem in black hole brick-wall model
• Entanglement entropy of round spheres
• Finite Temperature Effects for Massive Fields in D-dimensional Rindler-like Spaces
• Logarithmic correction to the Cardy-Verlinde formula in Topological Reissner-Nordström de Sitter Space
• Monodromy Defects in Free Field Theories
• Euclidean Approach to the Entropy for a Scalar Field in Rindler-like Space-Times
• Black hole entanglement entropy and the renormalization group
• Aspects of Warped AdS${}_3$/CFT${}_2$ Correspondence
• One-loop corrections for Schwarzschild black hole via 2D dilaton gravity
• Schwarzschild black hole as a grand canonical ensemble
• Black Hole Entropy and Gravity Cutoff
• Exact solution for a quantum field with $\delta$-like interaction
• Entropy of a Kerr-de Sitter black hole due to arbitrary spin fields
• Revisiting Leading Quantum Corrections to Near Extremal Black Hole Thermodynamics
• Newton constant, contact terms and entropy
• Logarithmic corrections to black hole entropy from Kerr/CFT
• Entropies of the general nonextreme stationary axisymmetric black hole: statistical mechanics and thermodynamics
• Geodesic Structure of the Quantum-Corrected Schwarzschild Black Hole Surrounded by Quintessence
• Large Field Inflation and Gravitational Entropy
• On the Entropy of a Quantum Field in the 2 + 1 Dimensional Spinning Black Holes
• Generalized 2d dilaton gravity with matter fields
• Log corrections to entropy of three dimensional black holes with soft hair
• Entanglement entropy and the Ricci flow
• Logarithmic terms in entropy of Schwarzschild black holes in higher loops
• Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity
• Quantum Scalar Field on the Massless (2+1)-Dimensional Black Hole Background
• Quantum bit threads
• Entanglement Entropy & Anomaly Inflow
• Logarithmic Corrections, Entanglement Entropy, and UV Cutoffs in de Sitter Spacetime
• Quantum field theory with and without conical singularities: Black holes with cosmological constant and the multi-horizon scenario
• Optical Approach for the Thermal Partition Function of Photons
• Self-forces in the Spacetime of Multiple Cosmic Strings
• Logarithmic correction to black hole entropy in universal low-energy string theory models
• Complexity-action of subregions with corners
• Black Hole Radiation with Modified Dispersion Relation in Tunneling Paradigm: Static Frame
• Quantum Hairs and Entropy of Quantum Isolated Horizon from Chern-Simons Theory
• Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
• Hawking Radiation Entropy and Horizon Divergences
• Logarithmic corrections to the entropy function of black holes in the open ensemble
• Interacting conformal scalar in a wedge
• Generalized Einstein-Maxwell theory: Seeley-DeWitt coefficients and logarithmic corrections to the entropy of extremal and non-extremal black holes
• Black hole as an Information Eraser
• Transplanckian Entanglement Entropy
• Logarithmic corrections to black hole entropy in matter coupled $\mathcal{N}\ge 1$ Einstein-Maxwell supergravity
• Thermodynamics of static and stationary black holes in Einstein-Gauss-Bonnet gravity with dark matter
• Nonextreme black holes near the extreme state and acceleration horizons: thermodynamics and quantum-corrected geometry
• Novel logarithmic corrections to black hole entropy
• Semi-infinite throats at finite temperature and static solutions in exactly solvable models of 2d dilaton gravity
• Entropy, topology of two-dimensional extreme black holes
• Logarithmic correction to the entropy of extremal black holes in $\mathcal{N}=1$ Einstein-Maxwell supergravity
• Entropy of A Scalar Field In (3 + 1)-dimensional Taub-NUT Space-Time
• Quantum states and their back-reacted geometries in 2d dilaton gravity
• Logarithmic corrections to the entropy of non-extremal black holes in $\mathcal{N}=1$ Einstein-Maxwell supergravity
• Holographic Entanglement Entropy of the Coulomb Branch
• Entropy discrepancy and total derivatives in trace anomaly
• Black Hole Radiation with Modified Dispersion Relation in Tunneling Paradigm: Free-fall Frame
• Finite Entanglement Entropy of Black Holes
• Wightman Functions' Behaviour on the Event Horizon of an Extremal Reissner-Nordström Black Hole
• Black holes in the conical ensemble
• On the renormalization of the Gibbons-Hawking boundary term
• Quantum extreme black holes at finite temperature and exactly solvable models of 2d dilaton gravity
• Euclidean methods and phase transitions for the strongest deformations compatible with Schwarzschild asymptotics
• Black hole thermodynamics from an ensemble-averaged theory
• Reduced quantum electrodynamics in curved space
• Relativistic Correction to Black Hole Entropy
• Minimal Length Effects on Entanglement Entropy of Spherically Symmetric Black Holes in Brick Wall Model
• Can the "brick wall" model present the same results in different coordinate representations?
• ADM mass of the quantum-corrected Schwarzchild black hole
• Logarithmic correction to the entropy of a Kerr-Newman family of black holes in $U(1{)}^2$-charged STU supergravity models
• Statistical ensembles and logarithmic corrections to black hole entropy
• Hybrid quantum states in 2d dilaton gravity
• Entanglement entropy between real and virtual particles in ${\varphi }^4$ quantum field theory
• Regular self-consistent geometries with infinite quantum backreaction in 2D dilaton gravity and black hole thermodynamics: unfamiliar features of familiar models
• Conformal bridge in a cosmic string background
• Finite Temperature Effective Potential for Gauge Models in de Sitter Space
• Emergence of quadratic gravity from entanglement equilibrium
• Entropy of scalar fields in 3+1 dimensional constant curvature black hole background
• A shell of Bosons in Spherically Symmetric spacetimes
• Quantum Holographic Entanglement Entropy to All Orders in $1/N$ Expansion
• Entanglement entropy between virtual and real excitations in quantum electrodynamics
• De Sitter entropy: on-shell versus off-shell
• Ambiguity in the evaluation of the effective action on the cone
• Exact Renormalization Group, Entanglement Entropy, and Black Hole Entropy
• Entanglement Entropy and Thermodynamics of Dynamical Black Holes
• Entanglement entropy due to near horizon degrees of freedom
• Entanglement entropy evolution during gravitational collapse
• Black Hole Entropy Sourced by String Winding Condensate
• Perturbative approach to the entanglement entropy and the area law in Fock and polymer quantization
• Gravity as a thermodynamic phenomenon
• Entanglement entropy for non-zero genus topologies
• Enhanced symmetry and Entropy of Schwarzschild-deSitter spacetime
• Aspects and applications of quantum field theory on spaces with conical singularities
• Note on explicit form of entanglement entropy in the RST model
• Off-shell phase diagram of BPS black holes in AdS${}_5$
• On the Renormalization of Entanglement Entropy
• Bulk entanglement and its shape dependence
• Black hole thermodynamics probes the equivalence principle
• Area law and OPE blocks in CFT
• Detect black holes using photons for coupling model of electromagnetic and gravitational fields
• Entanglement Entropy Evolution under Double-trace Deformation