Thermodynamics of topological black holes in Brans-Dicke gravity with a power-law Maxwell field

TL;DR

This paper derives new higher-dimensional topological black hole solutions in Brans-Dicke gravity with a power-law Maxwell field, analyzing their properties, thermodynamics, and conditions for horizon existence, including the impact of a negative cosmological constant.

Contribution

It introduces a conformal transformation approach to obtain exact solutions in Brans-Dicke theory with a power-law Maxwell field, and studies their thermodynamic properties and horizon conditions.

Findings

Existence of cosmological horizons with negative cosmological constant.

Entropy does not follow the area law.

Thermodynamic quantities are invariant under conformal transformation.

Abstract

In this paper, we present a new class of higher dimensional exact topological black hole solutions of the Brans-Dicke theory in the presence of a power-law Maxwell field as the matter source. For this aim, we introduce a conformal transformation which transforms the Einstein-dilaton-power-law Maxwell gravity Lagrangian to the Brans-Dicke-power-law Maxwell theory one. Then, by using this conformal transformation, we obtain the desired solutions. Next, we study the properties of the solutions and conditions under which we have black holes. Interestingly enough, we show that there is a cosmological horizon in the presence of a negative cosmological constant. Finally, we calculate the temperature and charge and then by calculating the Euclidean action, we obtain the mass, the entropy and the electromagnetic potential energy. We find that the entropy does not respect the area law, and also the conserved and thermodynamic quantities are invariant under conformal transformation. Using these thermodynamic and conserved quantities, we show that the first law of black hole thermodynamics is satisfied on the horizon.