Lifshitz Topological Black Holes

TL;DR

This paper introduces a class of Lifshitz black hole solutions in (3+1)D gravity with negative cosmological constant, exploring their thermodynamics and dual screening behavior in the context of holography.

Contribution

It presents new Lifshitz black hole solutions, including an exact case, and analyzes their thermodynamic and screening properties across different geometries.

Findings

Large black holes have similar thermodynamic behavior regardless of genus.

Small black holes exhibit distinct thermodynamic and screening properties.

An exact Lifshitz black hole solution is found for a specific parameter value.

Abstract

I find a class of black hole solutions to a (3+1) dimensional theory gravity coupled to abelian gauge fields with negative cosmological constant that has been proposed as the dual theory to a Lifshitz theory describing critical phenomena in (2+1) dimensions. These black holes are all asymptotic to a Lifshitz fixed point geometry and depend on a single parameter that determines both their area (or size) and their charge. Most of the solutions are obtained numerically, but an exact solution is also obtained for a particular value of this parameter. The thermodynamic behaviour of large black holes is almost the same regardless of genus, but differs considerably for small black holes. Screening behaviour is exhibited in the dual theory for any genus, but the critical length at which it sets in is genus-dependent for small black holes.