Lifshitz black holes in Brans-Dicke theory

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 $-(n-1)\mathrm{/}(n-2)\le \omega <-n\mathrm{/}(n-1)$. On the other hand, the no-ghost condition for the scalar field in the Einstein frame requires $0<z\le 2(n-2)\mathrm{/}(n-3)$. 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.