Thermodynamics of black branes in asymptotically Lifshitz spacetimes

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≥1. We continue our earlier work [G. Bertoldi, B. A. Burrington, and A. Peet, preceding Article, Phys. Rev. D 80, 126003 (2009).], exploring the thermodynamic properties of the “black brane” solutions with horizon topology R². We find that the black branes satisfy the relation E=(2)/(2+z)Ts where 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 (x₁,x₂)→λ(x₁,x₂), t→λ^zt.