Thermodynamics of Lovelock-Lifshitz Black Branes

TL;DR

This paper studies the thermodynamics of Lovelock-Lifshitz black branes, showing that key thermodynamic relations remain consistent with Einstein gravity despite differences in asymptotic behavior.

Contribution

It introduces a finite action for third order Lovelock gravity with a massive vector field and demonstrates that thermodynamic relations are unchanged from Einsteinian Lifshitz black branes.

Findings

Energy density computed via finite action method.

Conserved quantity relates horizon and infinity parameters.

Thermodynamic relations match Einsteinian Lifshitz case.

Abstract

We investigate the thermodynamics of Lovelock-Lifshitz black branes. We begin by introducing the finite action of third order Lovelock gravity in the presence of a massive vector field for a flat boundary, and use it to compute the energy density of these black branes. Using the field equations, we find a conserved quantity along the $r$ coordinate that relates the metric parameters at the horizon and at infinity. Remarkably, though the subleading large-$r$ behavior of Lovelock-Lifshitz black branes differs substantively from their Einsteinian Lifshitz counterparts, we find that the relationship between the energy density, temperature, and entropy density is unchanged from Einsteinian gravity. Using the first law of thermodynamics to obtain the relationship between entropy and temperature, we find that it too is the same as the Einsteinian case, apart from a constant of integration that depends on the Lovelock coefficients.