On Hořava-Lifshitz “black holes”

The most general spherically symmetric solution with zero shift is found in the non-projectable Hořava-Lifshitz class of theories with general coupling constants for the quadratic terms (with the Cotton tensor2 as the only cubic terms and without terms with derivatives of the lapse). It contains as special cases, spherically symmetric solutions found by other authors earlier. It is found that the generic solution has conventional (AdS, dS or flat) asymptotics with a universal 1/r tail. There are several special cases where the asymptotics differ, including the detailed balance choice of couplings. The conventional thermodynamics of this general class of solutions is established by calculating the energy, temperature and entropy. Although several of the solutions have conventional horizons, for particles with ultra-luminal dispersion relations such solutions appear to be horizonless.