Rotating Black Holes in Three-Dimensional Horava Gravity Revisited

Abstract: I revisit rotating black hole solutions in three-dimensional Horava gravity with z = 2 as a simpler set-up of the renormalizable quantum gravity a la Lifshitz and DeWitt. The solutions have a curvature singularity at the origin for a non-vanishing rotation parameter J, unlike the black holes in three-dimensional Einstein gravity. For anti-de Sitter space, there are black hole event horizons as usual and the singularity is not naked, in agreement with the cosmic censorship. On the other hand, for flat or de Sitter space, the earlier solution has also a cosmic-censorship problem because there are no conventional black hole horizons as in Einstein gravity, other than the usual cosmological horizon for the latter case, so that the singularity could be naked in Horava gravity. However, with the help of recent corrections, I show that the solutions have a peculiar black hole horizon at the origin so that the singularity is not naked even without the conventional black hole horizons in flat or de Sitter case, due to the Lorentz-violating higher-derivative terms. On the other hand, I note also that a new`cosmological" horizon exists even for the flat case, contrary to the usual wisdom, due to combined effects of the higher derivatives and the angular-momentum barrier. I study an unified treatment of their unusual black hole thermodynamics for the flat and de Sitter spaces, as well as the anti-de Sitter space, which might be due to lack of the absolute horizons in the Lorentz-violating gravity.