Holographic Superconductors with Lifshitz Scaling

TL;DR

This paper explores holographic superconductors in Lifshitz spacetime, revealing charged black holes with scalar hair and analyzing their geometric properties, contributing to understanding strongly coupled systems with anisotropic scaling.

Contribution

It introduces charged black holes with scalar hair in Lifshitz spacetime, extending holographic superconductor models to anisotropic scaling with z > 1.

Findings

Charged black holes with scalar hair are constructed.

Null curvature singularities are present in Lifshitz black holes.

The global geometry of Lifshitz black holes is analyzed.

Abstract

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 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.