Near-Horizon Conformal Symmetry and Black Hole Entropy in Any Dimension

Abstract

Recently, Carlip proposed a derivation of the entropy of the two-dimensional dilatonic black hole by investigating the Virasoro algebra associated with a newly introduced near-horizon conformal symmetry. We point out not only that the algebra of these conformal transformations is not well defined on the horizon, but also that the correct use of the eigenvalue of the operator $L_0$ yields vanishing entropy. It has been shown that these problems can be resolved by choosing a different basis of the conformal transformations which is regular even at the horizon. We also show the generalization of Carlip's derivation to any higher dimensional case in pure Einstein gravity. The entropy obtained is proportional to the area of the event horizon, but it also depends linearly on the product of the surface gravity and the parameter length of a horizon segment in consideration. We finally point out that this derivation of black hole entropy is quite different from the ones proposed so far, and several features of this method and some open issues are also discussed.

arXiv comment14 pages, no figure

References in corpus (35)

• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• The dS/CFT Correspondence
• Black Hole Entropy from Near-Horizon Microstates
• On Black Hole Entropy
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Black Hole Entropy from Conformal Field Theory in Any Dimension
• Mass, Entropy and Holography in Asymptotically de Sitter Spaces
• Entropy from Conformal Field Theory at Killing Horizons
• The Statistical Mechanics of the (2+1)-Dimensional Black Hole
• Conformal description of horizon's states
• Horizon Entropy
• Observables for Two-Dimensional Black Holes
• Statistical Entropy of Three-dimensional Kerr-De Sitter Space
• Near-Horizon Conformal Symmetry and Black Hole Entropy
• Boundary dynamics and the statistical mechanics of the 2+1 dimensional black hole
• Entropy of 2D black holes from counting microstates
• The Hamiltonian Dynamics of Bounded Spacetime and Black Hole Entropy: The Canonical Method
• Entropy of Three-Dimensional Black Holes in String Theory
• Asymptotic symmetries on Killing horizons
• Black hole entropy and thermodynamics from symmetries
• Near-Horizon Virasoro Symmetry and the Entropy of de Sitter Space in Any Dimension
• Black hole entropy calculations based on symmetries
• Comments on `` Black Hole Entropy from Conformal Field Theory in Any Dimension ''
• Holography, degenerate horizons and entropy
• Black hole entropy from classical Liouville theory
• Horizon conformal entropy in Gauss-Bonnet gravity
• Entropy of Killing horizons from Virasoro algebra in D-dimensional extended Gauss-Bonnet gravity
• Liouville Lost, Liouville Regained: Central Charge in a Dynamical Background
• Causal Boundary Entropy From Horizon Conformal Field Theory
• Reply to the comment by Park and Ho
• Comments on "Entropy of 2D Black Holes from Counting Microstates"
• Statistical Entropy of Schwarzschild Black Strings and Black Holes
• Higher curvature Lagrangians, conformal symmetry and microscopic entropy of Killing horizons
• The horizon and its charges in the first order gravity
• On Diffeomorphism Invariance and Black Hole Entropy

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• CFT Duals for Extreme Black Holes
• Lanczos-Lovelock models of gravity
• Kerr-AdS/CFT Correspondence in Diverse Dimensions
• Extremal Black Hole/CFT Correspondence in (Gauged) Supergravities
• Extremal Static AdS Black Hole/CFT Correspondence in Gauged Supergravities
• Dirty black holes: Symmetries at stationary non-static horizons
• BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and Statistical Entropy
• The Kerr/CFT correspondence and its extensions: a comprehensive review
• Kerr/CFT Correspondence in the Low Energy Limit of Heterotic String Theory
• A Comment on Kerr-CFT and Wald Entropy
• Noether Current, Horizon Virasoro Algebra and Entropy
• The CFT-interpolating Black Hole in Three Dimensions
• Holographic RG flow dual to attractor flow in extremal black holes
• A note on entropy of de Sitter black holes
• Thermodynamics of Exotic Black Holes, Negative Temperature, and Bekenstein-Hawking Entropy
• Near-Horizon BMS Symmetry, Dimensional Reduction, and Black Hole Entropy
• Conformal Symmetry for Rotating D-branes
• BTZ Black Hole with Higher Derivatives, the Second Law of Thermodynamics, and Statistical Entropy: A New Proposal
• Noether current of the surface term of Einstein-Hilbert action, Virasoro algebra and entropy
• Black Hole Thermodynamics from Euclidean Horizon Constraints
• Entropy and Temperature From Black-Hole/Near-Horizon-CFT Duality
• A Near Horizon CFT Dual for Kerr-Newman-$AdS$
• Testing Holographic Principle from Logarithmic and Higher Order Corrections to Black Hole Entropy
• Entropy of a generic null surface from its associated Virasoro algebra
• Conserved quantities and Virasoro algebra in New massive gravity
• Universal near-horizon conformal structure and black hole entropy
• 2D Gravity on $Ad{S}_2$ with Chern-Simons Corrections
• Black Hole Entropy and the Problem of Universality
• Black Holes as Conformal Field Theories on Horizons
• Dynamics of Diffeomorphism Degrees of Freedom at a Horizon
• Conformal entropy for generalised gravity theories as a consequence of horizon properties
• Holography in Three-dimensional Kerr-de Sitter Space with a Gravitational Chern-Simons Term
• Statistical entropy of the Schwarzschild black hole
• Conformal entropy from horizon states: Solodukhin's method for spherical, toroidal, and hyperbolic black holes in D-dimensional anti-de Sitter spacetimes
• Notes on the Area Theorem
• Gravitational anomalies and entropy
• Horizon Conformal Field Theories from $Ad{S}_2$ Black Holes
• Near-Extremal Black Hole Thermodynamics from AdS2/CFT1 Correspondence in The Low Energy Limit of 4D Heterotic String Theory
• Physics-to-gauge conversion at black hole horizons
• Liouville Theory on Horizons: Towards a Quantum Theory of Black Holes
• Hawking Radiation and Entropy from Horizon Degrees of Freedom
• Can One Understand Black Hole Entropy without Knowing Much about Quantum Gravity?
• Universal properties from local geometric structure of Killing horizon
• Statistical Mechanics of Three-dimensional Kerr-de Sitter Space
• Aspects of Diffeomorphism and Conformal invariance in classical Liouville theory
• A Dual CFT for Schwarzschild Black Hole
• Where are the BTZ Black Hole Degrees of Freedom? The Rotating Case
• On Quantum Microstates in the Near Extremal, Near Horizon Kerr Geometry
• On the Near Horizon Canonical Quantum Microstates from $Ad{S}_2/CF{T}_1$ and Conformal Weyl Gravity
• Near-Extremal Kerr AdS2xS2 Solution and Black-Hole/Near-Horizion-CFT Duality
• Horizons and the Thermal Harmonic Oscillator
• Black Hole Statistical Physics: Entropy
• Nöther Currents, Black Hole Entropy Universality and CFT Duality in Conformal Weyl Gravity
• Microscopic entropy of trapping horizon
• Surface charge of horizon symmetries of a black hole with supertranslation field