Holographic superconductors with Lifshitz scaling

Black holes in asymptotically Lifshitz spacetime provide a window onto finite temperature effects in strongly coupled Lifshitz models. We add a Maxwell gauge field and charged matter to a recently proposed gravity dual of (2+1)-dimensional Lifshitz theory. This gives rise to charged black holes with scalar hair, which correspond to the superconducting phase of holographic superconductors with z > 1 Lifshitz scaling. Along the way we analyze the global geometry of static, asymptotically Lifshitz black holes at the arbitrary critical exponent z > 1. In all known exact solutions there is a null curvature singularity in the black hole region, and, by a general argument, the same applies to generic Lifshitz black holes.