Born-Infeld Black Holes in (A)dS Spaces

TL;DR

This paper explores exact solutions of Einstein-Born-Infeld theory with a cosmological constant in higher dimensions, analyzing black hole thermodynamics, stability, and entropy, revealing conditions for stability and connections to the Cardy-Verlinde formula.

Contribution

It presents new exact solutions in higher-dimensional Einstein-Born-Infeld theory with detailed thermodynamic analysis and stability conditions, including a factorized solution involving product spaces.

Findings

Born-Infeld black holes with Ricci flat or hyperbolic horizons in AdS are always thermodynamically stable.

A critical Born-Infeld parameter exists for positive curvature horizons, determining stability.

Black hole and cosmological horizon entropies can be expressed via the Cardy-Verlinde formula.

Abstract

We study some exact solutions in a $D(\ge4)$-dimensional Einstein-Born-Infeld theory with a cosmological constant. These solutions are asymptotically de Sitter or anti-de Sitter, depending on the sign of the cosmological constant. Black hole horizon and cosmological horizon in these spacetimes can be a positive, zero or negative constant curvature hypersurface. We discuss the thermodynamics associated with black hole horizon and cosmological horizon. In particular we find that for the Born-Infeld black holes with Ricci flat or hyperbolic horizon in AdS space, they are always thermodynamically stable, and that for the case with a positive constant curvature, there is a critical value for the Born-Infeld parameter, above which the black hole is also always thermodynamically stable, and below which a unstable black hole phase appears. In addition, we show that although the Born-Infeld electrodynamics is non-linear, both black hole horizon entropy and cosmological horizon entropy can be expressed in terms of the Cardy-Verlinde formula. We also find a factorized solution in the Einstein-Born-Infeld theory, which is a direct product of two constant curvature spaces: one is a two-dimensional de Sitter or anti-de Sitter space, the other is a ($D-2$)-dimensional positive, zero or negative constant curvature space.