On Horava-Lifshitz "Black Holes"

TL;DR

This paper derives the most general spherically symmetric solutions in non-projectable Horava-Lifshitz gravity, analyzing their asymptotics, thermodynamics, and horizon properties, revealing novel horizonless solutions for ultra-luminal particles.

Contribution

It provides the first comprehensive derivation of spherically symmetric solutions in non-projectable Horava-Lifshitz gravity with general couplings, including thermodynamic analysis.

Findings

Most solutions have standard asymptotics with a universal 1/r tail.

Some solutions exhibit different asymptotics depending on couplings.

Certain horizon solutions are horizonless for ultra-luminal particles.

Abstract

The most general spherically symmetric solution with zero shift is found in the non-projectable Horava-Lifshitz class of theories with general coupling constants. 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.