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 ω and n. Asymptotic Lifshitz condition at infinity requires z > 1, which corresponds to − (n − 1)/(n − 2) ≤ ω < −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.
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