Isolated horizons in higher-dimensional Einstein-Gauss-Bonnet gravity

Abstract

The isolated horizon framework was introduced in order to provide a local description of black holes that are in equilibrium with their (possibly dynamic) environment. Over the past several years, the framework has been extended to include matter fields (dilaton, Yang-Mills etc) in D=4 dimensions and cosmological constant in $D\ge 3$ dimensions. In this article we present a further extension of the framework that includes black holes in higher-dimensional Einstein-Gauss-Bonnet (EGB) gravity. In particular, we construct a covariant phase space for EGB gravity in arbitrary dimensions which allows us to derive the first law. We find that the entropy of a weakly isolated and non-rotating horizon is given by $\mathcal{S}=(1/4G_D){\oint }_{S^{D-2}}\tilde{\mathbf{\epsilon }}(1+2\alpha \mathcal{R})$. In this expression $S^{D-2}$ is the $(D-2)$-dimensional cross section of the horizon with area form $\tilde{\mathbf{\epsilon }}$ and Ricci scalar $\mathcal{R}$, $G_D$ is the $D$-dimensional Newton constant and $\alpha$ is the Gauss-Bonnet parameter. This expression for the horizon entropy is in agreement with those predicted by the Euclidean and Noether charge methods. Thus we extend the isolated horizon framework beyond Einstein gravity.

18 pages; 1 figure; v2: 19 pages; 2 references added; v3: 19 pages; minor corrections; 1 reference added; to appear in Classical and Quantum Gravity

References in corpus (36)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Quantum Geometry and Black Hole Entropy
• Gauss-Bonnet Black Holes in AdS Spaces
• Brane-World Gravity
• Isolated and dynamical horizons and their applications
• Brane-world gravity
• On Black Hole Entropy
• Black Hole Thermodynamics and Negative Entropy in deSitter and Anti-deSitter Einstein-Gauss-Bonnet gravity
• The AdS/CFT Correspondence and a New Positive Energy Conjecture for General Relativity
• Black hole entropy from Quantum Geometry
• Isolated Horizons: Hamiltonian Evolution and the First Law
• Generic Isolated Horizons and their Applications
• Mechanics of Rotating Isolated Horizons
• Black hole boundaries
• A 3+1 perspective on null hypersurfaces and isolated horizons
• Black Holes of D=5 Supergravity
• Geometry of Generic Isolated Horizons
• Mechanics of Isolated Horizons
• Les Houches Lectures on De Sitter Space
• On Gauss-Bonnet black hole entropy
• Constant Curvature Black Holes
• Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations
• Bianchi identities in higher dimensions
• Extremal Isolated Horizons: A Local Uniqueness Theorem
• Ricci identities in higher dimensions
• Topological deformation of isolated horizons
• Non-minimally coupled scalar fields and isolated horizons
• Einstein-Yang-Mills Isolated Horizons: Phase Space, Mechanics, Hair and Conjectures
• Quasi-local rotating black holes in higher dimension: geometry
• Surface terms and the Gauss-Bonnet Hamiltonian
• Mechanics of multidimensional isolated horizons
• Laws Governing Isolated Horizons: Inclusion of Dilaton Couplings
• Horizon energy and angular momentum from a Hamiltonian perspective
• Astrophysical Implications of Higher-Dimensional Gravity
• Mechanics of higher-dimensional black holes in asymptotically anti-de Sitter space-times

Cited by in corpus (15)

• Black Holes in Loop Quantum Gravity
• Topological deformation of isolated horizons
• Dynamical black holes with symmetry in Einstein-Gauss-Bonnet gravity
• Black holes and black hole thermodynamics without event horizons
• Spacetime near isolated and dynamical trapping horizons
• Actions, topological terms and boundaries in first order gravity: A review
• Gauss-Bonnet black holes with non-constant curvature horizons
• Hamiltonian and Noether charges in first order gravity
• New Variables for Classical and Quantum Gravity in all Dimensions V. Isolated Horizon Boundary Degrees of Freedom
• Fundamental properties and applications of quasi-local black hole horizons
• Hamiltonian Formulation of Scalar Field Collapse in Einstein Gauss Bonnet Gravity
• Barbero-Immirzi parameter, manifold invariants and Euclidean path integrals
• Supersymmetric isolated horizons
• Neighbourhoods of Isolated Horizons and their stationarity
• The Entropy of Nonrotating Isolated Horizons in Lovelock Theory from Loop Quantum Gravity