Thermodynamics of higher dimensional topological dilaton black holes with power-law Maxwell field

TL;DR

This paper explores higher-dimensional topological dilaton black holes coupled with a power-law Maxwell field, analyzing their thermodynamics, stability, and the influence of nonlinear electromagnetic and dilaton fields on their properties.

Contribution

It introduces new solutions for Einstein-dilaton gravity with nonlinear Maxwell fields and investigates their thermodynamic and stability characteristics.

Findings

Solutions exist with three Liouville potentials for the dilaton.

The nonlinearity of the Maxwell field affects black hole thermodynamics.

Dilaton field influences the stability and physical properties of the black holes.

Abstract

In this paper, we extend the study on the nonlinear power-law Maxwell field to dilaton gravity. We introduce the $(n+1)$-dimensional action in which gravity is coupled to a dilaton and power-law nonlinear Maxwell field, and obtain the field equations by varying the action. We construct a new class of higher dimensional topological black hole solutions of Einstein-dilaton theory coupled to a power-law nonlinear Maxwell field and investigate the effects of the nonlinearity of the Maxwell source as well as the dilaton field on the properties of the spacetime. Interestingly enough, we find that the solutions exist provided one assumes three Liouville-type potentials for the dilaton field, and in case of the Maxwell field one of the Liouville potential vanishes. After studying the physical properties of the solutions, we compute the mass, charge, electric potential and temperature of the topological dilaton black holes. We also study thermodynamics and thermal stability of the solutions and disclose the effects of the dilaton field and the power-law Maxwell field on the thermodynamics of these black holes. Finally, we comment on the dynamical stability of the obtained solutions in four-dimensions.