Thermodynamics of Lifshitz Black Holes

TL;DR

This paper derives the thermodynamical first law for Lifshitz black holes using the Wald formalism, revealing unique properties such as super-extremal black holes with zero mass in Lifshitz spacetimes.

Contribution

It extends the Wald formalism to Lifshitz black holes and analyzes their thermodynamics, including cases with unusual properties like zero mass solutions.

Findings

First law for Lifshitz black holes derived and verified.

Existence of super-extremal charged black holes with zero mass.

Thermodynamics consistent with Lifshitz spacetime properties.

Abstract

We specialize the Wald formalism to derive the thermodynamical first law for static black holes with spherical/torus/hyperbolic symmetries in a variety of supergravities or supergravity-inspired theories involving multiple scalars and vectors. We apply the formula to study the first law of a general class of Lifshitz black holes. We analyse the first law of three exact Lifshitz black holes and the results fit the general pattern. In one example, the first law is $TdS + \Phi dQ=0$ where $(\Phi,Q)$ are the electric potential and charge of the Maxwell field. The unusual vanishing of mass in this specific solution demonstrates that super-extremal charged black holes can exist in asymptotic Lifshitz spacetimes.