Thermodynamics of Einstein-Born-Infeld black holes with negative cosmological constant

Abstract

We study the thermodynamics associated to topological black hole solutions of AdS gravity coupled to nonlinear electrodynamics (Born-Infeld) in any dimension, using a background-independent regularization prescription for the Euclidean action given by boundary terms which explicitly depend on the extrinsic curvature (Kounterterms series). A finite action principle leads to the correct definition of thermodynamic variables as Noether charges, which satisfy a Smarr-like relation. In particular, for the odd-dimensional case, a consistent thermodynamic description is achieved if the internal energy of the system includes the vacuum energy for AdS spacetime.

29 pages, no figures; additional comments on extreme black hole case, a few references added; final version for PRD

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• Universal regularization prescription for Lovelock AdS gravity
• Vacuum energy in Einstein-Gauss-Bonnet AdS gravity
• Counterterms in Dimensionally Continued AdS Gravity
• On boundary conditions in three-dimensional AdS gravity
• Thermodynamics of rotating black branes in $(n+1)$-dimensional Einstein-Born-Infeld gravity
• Black holes and singularities in string theory

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