Thermodynamics of black branes in asymptotically Lifshitz spacetimes

TL;DR

This paper investigates the thermodynamic properties of black branes in asymptotically Lifshitz spacetimes, revealing a specific energy-temperature-entropy relation consistent with dual 2+1 dimensional critical theories.

Contribution

It extends previous work by analyzing thermodynamics of Lifshitz black branes and deriving a key energy relation aligned with scaling symmetries.

Findings

Black branes satisfy the relation b4a0=a0(2/2+z)Ts

Results match expected behavior for 2+1D Lifshitz theories

Supports holographic duality for critical phenomena

Abstract

Recently, a class of gravitational backgrounds in 3+1 dimensions have been proposed as holographic duals to a Lifshitz theory describing critical phenomena in 2+1 dimensions with critical exponent $z\geq 1$. We continue our earlier work \cite{Bertoldi:2009vn}, exploring the thermodynamic properties of the "black brane" solutions with horizon topology $\mathbb{R}^2$. We find that the black branes satisfy the relation $\mathcal{E}=\frac{2}{2+z}Ts$ where $\mathcal{E}$ is the energy density, $T$ is the temperature, and $s$ is the entropy density. This matches the expected behavior for a 2+1 dimensional theory with a scaling symmetry $(x_1,x_2)\to \lambda (x_1,x_2)$, $t\to \lambda^z t$.