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, $E=\frac{2}{z+2}TS$, is also satisfied for universal horizons, including the correct $z$ scaling.

7 pages

References in corpus (11)

• Quantum Gravity at a Lifshitz Point
• Quantum Criticality in Heavy Fermion Metals
• Membranes at Quantum Criticality
• Heavy Fermions and Quantum Phase Transitions
• Horava-Lifshitz gravity: a status report
• Lifshitz Gravity for Lifshitz Holography
• Towards thermodynamics of universal horizons in Einstein-æther theory
• Universal horizons in maximally symmetric spaces
• Log corrections to entropy of three dimensional black holes with soft hair
• On the first law of black holes with a universal horizon
• Anisotropic Scale Invariant Spacetimes and Black Holes in Zwei-Dreibein Gravity

Cited by in corpus (1)

• The Horava-Lifshitz Modifications of the Casimir effect at finite temperature revisted