The Rotating Black Hole in Renormalizable Quantum Gravity: The Three-Dimensional Hořava Gravity Case

Abstract

Recently Hořava proposed a renormalizable quantum gravity, without the ghost problem, by abandoning Einstein's equal-footing treatment of space and time through the anisotropic scaling dimensions. Since then various interesting aspects, including the exact black hole solutions have been studied but no "rotating" black hole solutions have been found yet, except some limiting cases. In order to fill the gap, I consider a simpler three-dimensional set-up with z=2 and obtain the exact rotating black hole solution. This solution has a ring curvature singularity inside the outer horizon, like the four- dimensional Kerr black hole in Einstein gravity, as well as a curvature singularity at the origin. The usual mass bound works also here but in a modified form. Moreover, it is shown that the conventional first law of thermodynamics with the usual Hawking temperature and chemical potential does not work, which seems to be the genuine effect of Lorentz-violating gravity due to lack of the absolute horizon.

Some more elaborate discussions on the thermodynamics issue, the failure of the usual black hole thermodynamics, in the last paragraph of Sec. IV, Typos Corrected, 11 pages, 3 figures, Accepted in PLB

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Cited by in corpus (10)

• Hořava Gravity at a Lifshitz Point: A Progress Report
• Rotating black holes in three-dimensional Hořava gravity
• Lifshitz spacetimes, solitons, and generalized BTZ black holes in quantum gravity at a Lifshitz point
• High-dimensional Lifshitz-type spacetimes, universal horizons and black holes in Hořava-Lifshitz gravity
• Two Dimensional Horava-Lifshitz Black Hole Solutions
• The Hamiltonian Dynamics of Horava Gravity
• Complete Classification of Four-Dimensional Black Hole and Membrane Solutions in IR-modified Hořava Gravity
• A Remark on Polar Noncommutativity
• Asymptotic flatness and nonflat solutions in the critical 2+1 Horava theory
• Rotating Black Holes in Three-Dimensional Horava Gravity Revisited