Thermodynamics of Regular Black Holes in Anti-de Sitter Space

TL;DR

This paper constructs and analyzes regular black holes with anti-de Sitter asymptotics in higher dimensions, exploring their thermodynamics, stability, and electromagnetic properties, including new fully regular solutions with diverse core geometries.

Contribution

It introduces a general framework for regular black holes in AdS space with higher-order curvature corrections and provides the first fully regular solutions with nonlinear electrodynamics.

Findings

Regular black branes are inner-extremal, potentially avoiding inner horizon instabilities.

Fully regular solutions are found for nonlinear electrodynamics, with core geometry determined by mass and charge ratios.

Black hole thermodynamics shows fluid-like behavior with a finite molecular volume due to regularization.

Abstract

We construct regular black holes with anti-de Sitter asymptotics in theories incorporating infinite towers of higher-order curvature corrections in any dimension $D \ge 5$. We find that regular black branes are generically inner-extremal, potentially evading instabilities typically associated with inner horizons. Considering minimally coupled matter, we establish general criteria for the existence of singularity-free solutions. We analyze solutions coupled to Maxwell and nonlinear (Born--Infeld and RegMax) electrodynamics, demonstrating in the latter case the first examples of fully regular gravitational and electromagnetic fields for all parameter values. Here, we find that the ratio of the gravitational mass to the electrostatic self-energy determines whether the regular core is de Sitter or anti-de Sitter. We perform a detailed analysis of the black hole thermodynamics and show that the equation of state exhibits features akin to those of fluids with a finite molecular volume induced by the regularization parameter.