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 R-2. We find that the black branes satisfy the relation epsilon = 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 (x(1), x(2)) -> lambda(x(1), x(2)), t -> lambda(z)t.