Lifshitz black holes in Brans-Dicke theory

Abstract

We present an exact asymptotically Lifshitz black hole solution in Brans-Dicke theory of gravity in arbitrary n(≥ 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 ! and n. Asymptotic Lifshitz condition at infinity requires z > 1, which corresponds to ?(n ? 1)/(n ? 2) ≥ w ?n/(n ? 1). On the other hand, the no-ghost condition for the scalar field in the Einstein frame requires 0 < z ≤ 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. © 2011 SISSA.