Energy-entropy relation for asymptotically Lifshitz spacetimes with universal horizons
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=2z+2TS, is also satisfied for universal horizons, including the correct z scaling.
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