Rotating black holes in 3D Hořava gravity revisited

Abstract

Abstract I revisit rotating black hole solutions in 3D Hořava gravity with z = 2 as a simpler set-up of the renormalizable quantum gravity à la Lifshitz [Zh. Eksp. Teor. Fiz. 11, 255 (1941)] and DeWitt [Phys. Rev. 160, 1113 (1967)]. The solutions have a curvature singularity at the origin for a non-vanishing rotation parameter ${\cal J}$, unlike the black holes in 3D Einstein gravity. For anti-de Sitter space, there are black hole event horizons as usual and the singularity is not naked, in agreement with cosmic censorship. On the other hand, for flat or de Sitter space, the earlier solution also has 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 Hořava 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 the flat or de Sitter cases, due to Lorentz-violating higher-derivative terms. On the other hand, I also note that a new “cosmological” horizon exists even for the flat case, contrary to the usual wisdom, due to the combined effects of the higher derivatives and the angular-momentum barrier. I study a 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 the lack of absolute horizons in Lorentz-violating gravity.