Thermodynamics of black branes in asymptotically Lifshitz spacetimes

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 $z\ge 1$. 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 $(x_1,x_2)\to \lambda (x_1,x_2)$, $t\to {\lambda }^{z}t$.

8 pages, references added and regrouped

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