Rotating Black Branes in Brans-Dicke-Born-Infeld Theory

TL;DR

This paper introduces a new class of charged rotating black brane solutions in higher-dimensional Brans-Dicke-Born-Infeld theory, analyzing their properties, thermodynamics, and deviations from the area law.

Contribution

It provides explicit solutions for black branes in this theory using a conformal transformation, and explores their thermodynamic behavior and geometric properties.

Findings

Solutions include black branes, extremal black branes, or naked singularities.

Black branes are neither asymptotically flat nor AdS.

Entropy does not follow the area law.

Abstract

In this paper, we present a new class of charged rotating black brane solutions in the higher dimensional Brans-Dicke-Born-Infeld theory and investigate their properties. Solving the field equations directly is a non-trivial task because they include the second derivatives of the scalar field. We remove this difficulty through a conformal transformation. Also, we find that the suitable Lagrangian of Einstein-Born-Infeld-dilaton gravity is not the same as presented in \cite{DHSR}. We show that the given 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. These black brane solutions are neither asymptotically flat nor (anti)-de Sitter. Then we calculate finite Euclidean action, the conserved and thermodynamic quantities through the use of counterterm method. Finally, we argue that these quantities satisfy the first law of thermodynamics, and the entropy does not follow the area law.