Thermodynamical properties of topological Born-Infeld-dilaton black holes

TL;DR

This paper presents new analytic solutions for topological black holes in higher dimensions within a theory coupling gravity, Born-Infeld nonlinear electrodynamics, and a dilaton field, exploring their unusual asymptotics and thermodynamic stability.

Contribution

It introduces novel $(n+1)$-dimensional topological dilaton black hole solutions with nonlinear electrodynamics and analyzes their thermodynamics and stability.

Findings

Black holes have non-standard asymptotics, neither flat nor AdS.

Event horizons can have positive, zero, or negative curvature.

Dilaton and Born-Infeld fields influence thermal stability.

Abstract

We examine the $(n+1)$-dimensional $(n\geq3)$ action in which gravity is coupled to the Born-Infeld nonlinear electrodynamic and a dilaton field. We construct a new $(n+1)$-dimensional analytic solution of this theory in the presence of Liouville-type dilaton potentials. These solutions which describe charged topological dilaton black holes with nonlinear electrodynamics, have unusual asymptotics. They are neither asymptotically flat nor (anti)-de Sitter. The event horizons of these black holes can be an $(n-1)$-dimensional positive, zero or negative constant curvature hypersurface. We also analyze thermodynamics and stability of these solutions and disclose the effect of the dilaton and Born-Infeld fields on the thermal stability in the canonical ensemble.