Thermodynamics of charged rotating black branes in Brans-Dicke theory with quadratic scalar field potential

TL;DR

This paper constructs and analyzes charged rotating black brane solutions in higher-dimensional Brans-Dicke theory with a quadratic scalar potential, revealing unique thermodynamic properties and horizon structures.

Contribution

It introduces new charged rotating black brane solutions in Brans-Dicke theory with a quadratic potential and studies their thermodynamics and horizon characteristics.

Findings

Solutions can be black branes, extremal, or naked singularities.

Thermodynamic quantities satisfy the first law.

Entropy does not follow the area law.

Abstract

We construct a class of charged rotating solutions in $(n+1)$-dimensional Maxwell-Brans-Dicke theory with flat horizon in the presence of a quadratic potential and investigate their properties. These solutions are neither asymptotically flat nor (anti)-de Sitter. We find that these solutions can present black brane, with inner and outer event horizons, an extreme black brane or a naked singularity provided the parameters of the solutions are chosen suitably. We compute the finite Euclidean action through the use of counterterm method, and obtain the conserved and thermodynamic quantities by using the relation between the action and free energy in grand-canonical ensemble. We find that these quantities satisfy the first law of thermodynamics, and the entropy does not follow the area law.