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

TL;DR

This paper investigates the thermodynamics of Einstein-Born-Infeld black holes in Anti-de Sitter space across various dimensions, employing a boundary term regularization to accurately define thermodynamic quantities and relations.

Contribution

It introduces a boundary term regularization method for the Euclidean action that ensures a consistent thermodynamic description of AdS black holes with nonlinear electrodynamics.

Findings

Thermodynamic variables are correctly derived as Noether charges.

A Smarr-like relation is satisfied in the thermodynamic framework.

Including vacuum energy yields a consistent thermodynamic description in odd dimensions.

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.