Energy-entropy relation for asymptotically Lifshitz spacetimes with universal horizons

TL;DR

This paper numerically investigates universal horizons in 2+1 dimensional Lifshitz spacetimes within Horava-Lifshitz gravity, confirming thermodynamic laws and energy-entropy relations across multiple dynamical exponents.

Contribution

It provides the first numerical solutions for universal horizons in Lifshitz spacetimes for various z and verifies their thermodynamic consistency and expected energy-entropy scaling.

Findings

Universal horizons satisfy a thermodynamic first law.

Smarr formula holds for all studied z.

Energy-entropy relation matches Lifshitz field theory expectations.

Abstract

We numerically solve for 2+1 asymptotically Lifshitz universal horizon solutions in Horava-Lifshitz gravity for dynamical exponents $z=2$ through $z=8$. We find that for all $z$ there is a thermodynamical first law and Smarr formula. Furthermore, we find that the energy-entropy relation expected for a thermal state in a two dimensional Lifshitz field theory, $E=\frac{2}{z+2}TS$, is also satisfied for universal horizons, including the correct $z$ scaling.