Lifshitz black holes in Brans-Dicke theory

TL;DR

This paper derives exact Lifshitz black hole solutions in Brans-Dicke gravity across multiple dimensions, analyzing their properties, thermodynamics, and extensions with charge, revealing conditions on parameters for physical viability.

Contribution

It provides the first exact Lifshitz black hole solutions in Brans-Dicke theory with detailed parameter constraints and thermodynamic analysis.

Findings

Lifshitz black hole solutions exist for specific parameter ranges

Hawking temperature and thermodynamics are computed and discussed

Charged solutions under Maxwell field are also constructed

Abstract

We present an exact asymptotically Lifshitz black hole solution in Brans-Dicke theory of gravity in arbitrary $n(\ge 3)$ dimensions in presence of a power-law potential. In this solution, the dynamical exponent $z$ is determined in terms of the Brans-Dicke parameter $\omega$ and $n$. Asymptotic Lifshitz condition at infinity requires $z>1$, which corresponds to $-(n-1)/(n-2) \le \omega < -n/(n-1)$. On the other hand, the no-ghost condition for the scalar field in the Einstein frame requires $0<z \le 2(n-2)/(n-3)$. We compute the Hawking temperature of the black hole solution and discuss the problems encountered and the proposals in defining its thermodynamic properties. A generalized solution charged under the Maxwell field is also presented.