Thermal Fields, Entropy, and Black Holes

Abstract

In this review we describe statistical mechanics of quantum systems in the presence of a Killing horizon and compare statistical-mechanical and one-loop contributions to black hole entropy. Studying these questions was motivated by attempts to explain the entropy of black holes as a statistical-mechanical entropy of quantum fields propagating near the black hole horizon. We provide an introduction to this field of research and review its results. In particular, we discuss the relation between the statistical-mechanical entropy of quantum fields and the Bekenstein-Hawking entropy in the standard scheme with renormalization of gravitational coupling constants and in the theories of induced gravity.

44 pages, LaTeX file

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• Dilaton Gravity in Two Dimensions
• Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
• Superfluid analogies of cosmological phenomena
• A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
• Statistical Entropy of a Stationary Dilaton Black Hole from Cardy Formula
• Black holes, brick walls and the Boulware state
• Heat Kernel Expansion for Semitransparent Boundaries
• Geometric entropy, area, and strong subadditivity
• Effect of spins on the quantum entropy of black holes
• Finite temperature nonlocal effective action for quantum fields in curved space
• Entanglement Entropy in Critical Phenomena and Analogue Models of Quantum Gravity
• A proof of the generalized second law for rapidly-evolving Rindler horizons
• Entanglement Interpretation of Black Hole Entropy in String Theory
• Ten Proofs of the Generalized Second Law
• Generalized second law at linear order for actions that are functions of Lovelock densities
• Entropy, Contact Interaction with Horizon and Dark Energy
• Quantum entropy of the Kerr black hole arising from gravitational perturbation
• Five Problems in Quantum Gravity
• Renormalization of Entanglement Entropy and the Gravitational Effective Action
• Black Hole Thermodynamics from Near-Horizon Conformal Quantum Mechanics
• Area terms in entanglement entropy
• Quantum entropy of the general non-extreme stationary axisymmetric black hole due to minimally coupled quantum scalar field
• Entanglement Entropy in Quantum Gravity and the Plateau Problem
• Black hole entropy from entanglement: A review
• On the generalized entropy pseudoadditivity for complex systems
• Black hole entanglement entropy and the renormalization group
• Superradiance and the Statistical-Mechanical Entropy of Rotating BTZ Black Holes
• Quantum Properties of Topological Black Holes
• Heat Kernel Expansions for Distributional Backgrounds
• Semiclassical Methods in Curved Spacetime and Black Hole Thermodynamics
• Entropy of a Kerr-de Sitter black hole due to arbitrary spin fields
• Reissner-Nordström-AdS black hole in the GEMS approach
• Entropies of Rotating Charged Black Holes from Conformal Field Theory at Killing Horizons
• Black Hole Entropy in Induced Gravity: Reduction to 2D Quantum Field Theory on the Horizon
• Entropies of the general nonextreme stationary axisymmetric black hole: statistical mechanics and thermodynamics
• Sub-leading contributions to the black hole entropy in the brick wall approach
• Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect
• Thermodynamics and Statistical Mechanics of Induced Liouville Gravity
• Statistical Mechanics on Axially-symmetric Space-times with the Killing Horizon and Entropy of Rotating Black Holes in Induced Gravity
• Entropy of the Randall-Sundrum black brane world in the brick-wall method
• Higher dimensional flat embeddings of (2+1) dimensional black holes
• Brick Walls on the Brane
• Statistical Mechanics, Gravity, and Euclidean Theory
• Black Hole Scattering and Partition Functions
• The a-theorem and entanglement entropy
• Ultrastatic spacetimes
• One-to-one correspondence between entanglement mechanics and black hole thermodynamics
• Conformal Tightness of Holographic Scaling in Black Hole Thermodynamics
• Kaluza-Klein Method in Theory of Rotating Quantum Fields
• Entropy of a box of gas in an external gravitational field $-$ revisited
• Horizon entanglement area law from regular black hole thermodynamics
• `Thermodynamics' of Minimal Surfaces and Entropic Origin of Gravity
• Dimensional reduction from entanglement in Minkowski space
• Moving-mirror entropy
• Lodged in the throat: Internal infinities and AdS/CFT
• A holographic bound on the total number of computations in the visible Universe
• Remarks on 't Hooft's Brick Wall Model
• Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
• Generalised second law beyond the semiclassical regime
• Statistical Mechanics of Charged Black Holes in Induced Einstein-Maxwell Gravity
• Can the "brick wall" model present the same results in different coordinate representations?
• Is the Euclidean path integral always equal to the thermal partition function?
• Conformal Enhancement of Holographic Scaling in Black Hole Thermodynamics: A Near-Horizon Heat-Kernel Framework
• Can One Understand Black Hole Entropy without Knowing Much about Quantum Gravity?
• Higher order WKB corrections to black hole entropy in brick wall formalism
• Boiling Quantum Vacuum: Thermal Subsystems from Ground-State Entanglement
• Entropy of BTZ black strings in the brick wall approach
• Microcanonical statistics of black holes and bootstrap condition
• De Sitter entropy: on-shell versus off-shell
• On the resilience of the gravitational variational principle under renormalization
• Near-Horizon Geometry and the Entropy of a Minimally Coupled Scalar Field in the Schwarzschild Black Hole
• Ambiguity in the evaluation of the effective action on the cone
• Near-Horizon Geometry and the Entropy of a Minimally Coupled Scalar Field in the Kerr Black Hole
• Revision of the brick wall method for calculating the black hole thermodynamic quantities
• Aspects and applications of quantum field theory on spaces with conical singularities
• Noncommutative corrections to the minimal surface areas of the pure AdS spacetime and Schwarzschild-AdS black hole
• Synthetic horizons in an atomic chain: Horizon-induced effects and connections to quantum Hall systems