Quasilocal Thermodynamics of Kerr and Kerr-anti-de Sitter Spacetimes and the AdS/CFT Correspondence

Abstract

We consider the quasilocal thermodynamics of rotating black holes in asymptotically flat and asymptotically anti de Sitter spacetimes. Using the minimal number of intrinsic boundary counterterms inspired by the AdS/CFT correspondence, we find that we are able to carry out an analysis of the thermodynamics of these black holes for virtually all possible values of the rotation parameter and cosmological constant that leave the quasilocal boundary well-defined, going well beyond what is possible with background subtraction methods. Specifically, we compute the quasilocal energy $E$ and angular momentum $J$ for arbitrary values of the rotation, mass and cosmological constant parameters for the 3+1 dimensional Kerr, Kerr-AdS black holes and 2+1 dimensional BTZ black hole. We perform a quasilocal stability analysis and find phase behavior that is commensurate with previous analyses carried out at infinity.

arXiv commentLatex, 43 pages, 22 eps figures, several typos corrected, final version to appear in Phys. Rev. D

References in corpus (26)

• The Black Hole in Three Dimensional Space Time
• A Stress Tensor for Anti-de Sitter Gravity
• The Holographic Weyl anomaly
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Geometry of the 2+1 Black Hole
• Thermodynamics of Kerr-Newman-AdS Black Holes and Conformal Field Theories
• Surface Terms as Counterterms in the AdS/CFT Correspondence
• Temperature, Energy, and Heat Capacity of Asymptotically Anti-De Sitter Black Holes
• Asymptotically Anti-de Sitter Space-times: Conserved Quantities
• The Gravitational Action in Asymptotically AdS and Flat Spacetimes
• Misner String Entropy
• Nut Charge, Anti-de Sitter Space and Entropy
• Gravitational Entropy and Global Structure
• Solitonic Black Holes in Gauged N=2 Supergravity
• Entropy of Rotating Misner String Spacetimes
• Conserved Quantities in Kerr-anti-de Sitter Spacetimes in Various Dimensions
• Moving Observers, Non-orthogonal Boundaries, and Quasilocal Energies
• Holographic Stress Tensors for Kerr-AdS Black Holes
• Statistical Entropy and AdS/CFT Correspondence in BTZ Black Holes
• Lightcone reference for total gravitational energy
• Quasilocal Energy for a Kerr black hole
• Conserved masses in GHS Einstein and string black holes
• Noether Charges, Brown-York Quasilocal Energy and Related Topics
• A quasilocal calculation of tidal heating
• How to make the gravitational action on non-compact space finite
• Gravitational Calorimetry

Cited by in corpus (42)

• Energy and angular momentum of the gravitational field in the teleparallel geometry
• Hawking radiation from rotating black holes in anti-de Sitter spaces via gauge and gravitational anomalies
• Action, Mass and Entropy of Schwarzschild-de Sitter black holes and the de Sitter/CFT Correspondence
• Thermodynamics of Rotating Black Branes in Gauss-Bonnet-nonlinear Maxwell Gravity
• Thermodynamics of Rotating Charged Black Branes in Third Order Lovelock Gravity and the Counterterm Method
• Thermodynamics of higher dimensional topological charged AdS black branes in dilaton gravity
• Topological Black Holes in Gauss-Bonnet Gravity with conformally invariant Maxwell source
• Extremality conditions for isolated and dynamical horizons
• Thermodynamics of Rotating Charged Black Strings and (A)dS/CFT Correspondence
• On classical super-radiance in Kerr-Newman-anti-de Sitter black holes
• Note on counterterms in asymptotically flat spacetimes
• Counterterm Method in Lovelock Theory and Horizonless Solutions in Dimensionally Continued Gravity
• Thermodynamics of d-dimensional charged rotating black brane and AdS/CFT correspondence
• Magnetic Branes in Gauss-Bonnet Gravity
• Thermodynamics of Rotating Solutions in Gauss-Bonnet-Maxwell Gravity and the Counterterm Method
• Quasilocal Thermodynamics of Kerr de Sitter Spacetimes and the dS/CFT Correspondence
• Rotating Topological Black Branes in Various Dimensions and AdS/CFT Correspondence
• Thermodynamics, geometrothermodynamics and critical behavior of (2+1)-dimensional black holes
• Thermodynamics of a Kerr Newman de Sitter Black Hole
• On the gravitational energy of the Kaluza Klein monopole
• Thermodynamic instability of topological black holes with nonlinear source
• Magnetic String Coupled to Nonlinear Electromagnetic Field
• Three dimensional nonlinear magnetic AdS solutions through topological defects
• Entropy of a Kerr-de Sitter black hole due to arbitrary spin fields
• Kerr de Sitter Spacetimes in Various Dimension and dS/CFT Correspondence
• Horizonless Rotating Solutions in $(n+1)$-dimensional Einstein-Maxwell Gravity
• Entropy and Mass Bounds of Kerr-de Sitter Spacetimes
• Thermodynamics of Taub-NUT Black Holes in Einstein-Maxwell Gravity
• Thermodynamics of Dual CFTs for Kerr-AdS Black Holes
• Scale-invariant rotating black holes in quadratic gravity
• Rotating charged black hole with Weyl corrections
• Gravitational Energy of Kerr and Kerr Anti-de Sitter Space-times in the Teleparallel Geometry
• Quartic Quasi-Topological-Born-Infeld Gravity
• Local thermodynamics of KS black hole
• Gravitational energy, gravitational pressure, and the thermodynamics of a charged black hole in teleparallel gravity
• Nonlinear Charged Black Holes in Anti-de Sitter Quasi-Topological Gravity
• Phase transitions and thermodynamic geometry of a Kerr-Newman black hole in a cavity
• Asymptotically AdS Magnetic Branes in (n+1)-dimensional Dilaton Gravity
• Quasi-Topological Magnetic Brane coupled to Nonlinear Electrodynamics
• Counterterms for Static Lovelock Solutions
• Regular $(2+1)$-dimensional spatially homogeneous ${\alpha }^{\prime }$-corrected BTZ-like black hole in string theory
• Duality of Quasilocal Gravitational Energy and Charges with Non-orthogonal Boundaries