Analytic Lifshitz black holes in higher dimensions

Abstract

We generalize the four-dimensional R2-corrected z = 3/2 Lifshitz black hole to a two-parameter family of black hole solutions for any dynamical exponent z and for any dimension D. For a particular relation between the parameters, we find the first example of an extremal Lifshitz black hole. An asymptotically Lifshitz black hole with a logarithmic decay is also exhibited for a specific critical exponent depending on the dimension. We extend this analysis to the more general quadratic curvature corrections for which we present three new families of higher-dimensional D ≥ 5 analytic Lifshitz black holes for generic z. One of these higher-dimensional families contains as critical limits the z = 3 three-dimensional Lifshitz black hole and a new z = 6 four-dimensional black hole. The variety of analytic solutions presented here encourages to explore these gravity models within the context of non-relativistic holographic correspondence.