Analytic Lifshitz black holes in higher dimensions

TL;DR

This work constructs analytic Lifshitz black holes in gravity theories with quadratic curvature corrections across arbitrary dimensions. It first presents a two-parameter, $R^2$-corrected Lifshitz black hole family for any dimension and dynamical exponent $z$, including an extremal example and a logarithmic fall-off at a critical $z=z_+$, with a perfect-square form of the action highlighting a degeneracy in constant-curvature sectors. It then extends to the most general quadratic invariants, yielding three new higher-dimensional ($D\ge5$) Lifshitz black hole families for generic $z$, and identifies conformal limits and notable reductions to well-known models (e.g., New Massive Gravity in $D=3$ and a $z=6$ solution in $D=4$). The paper also analyzes critical lower-dimensional limits via dimensional continuation, uncovering a three-dimensional Lifshitz black hole with $z=3$ and a novel four-dimensional Lifshitz black hole with $z=6$, while noting that other families do not admit regular $D=4$ limits. Overall, the results enrich the landscape of analytic Lifshitz spacetimes and provide a broad platform for exploring non-relativistic holography in higher-curvature gravity theories.

Abstract

We generalize the four-dimensional R^2-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.