Constant curvature black holes in Einstein AdS gravity: Euclidean action and thermodynamics

Abstract

We compute the Euclidean action for constant curvature black holes (CCBHs), as an attempt to associate thermodynamic quantities to these solutions of Einstein anti-de Sitter (AdS) gravity. CCBHs are gravitational configurations obtained by identifications along isometries of a $D$-dimensional globally AdS space, such that the Riemann tensor remains constant. Here, these solutions are interpreted as extended objects, which contain a $(D-2)$-dimensional de-Sitter brane as a subspace. Nevertheless, the computation of the free energy for these solutions shows that they do not obey standard thermodynamic relations.

arXiv comment13 pages, no figures, one reference added, final version for PRD

References in corpus (19)

• The Black Hole in Three Dimensional Space Time
• Black Hole Entropy is Noether Charge
• A Stress Tensor for Anti-de Sitter Gravity
• Geometry of the 2+1 Black Hole
• Enthalpy and the Mechanics of AdS Black Holes
• Ricci flow with surgery on three-manifolds
• Surface Terms as Counterterms in the AdS/CFT Correspondence
• Thermodynamics of Asymptotically Locally AdS Spacetimes
• Black Hole Chemistry
• Mass, Angular Momentum and Thermodynamics in Four-Dimensional Kerr-AdS Black Holes
• Topological regularization and self-duality in four-dimensional anti-de Sitter gravity
• Black Holes and Wormholes in 2+1 Dimensions
• Constant Curvature Black Holes
• Regularization of odd-dimensional AdS gravity: Kounterterms
• Conserved charges for black holes in Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics in AdS space
• Black Holes and Causal Structure in Anti-de Sitter Isometric Spacetimes
• On the negative spectrum of the 2+1 black hole
• Entropy of Constant Curvature Black Holes in General Relativity
• Constant curvature black holes in Einstein AdS gravity: conserved quantities

Cited by in corpus (1)

• Higher spin fluctuations on spinless 4D BTZ black hole