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.

arXiv commentChanged title, Added comments, 16 pages, 7 figures

References in corpus (45)

• The Black Hole in Three Dimensional Space Time
• Quantum Gravity at a Lifshitz Point
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Eternal Black Holes in AdS
• Cool horizons for entangled black holes
• The dS/CFT Correspondence
• Massive Gravity in Three Dimensions
• Membranes at Quantum Criticality
• A healthy extension of Horava gravity
• Mass, Entropy and Holography in Asymptotically de Sitter Spaces
• A New Cosmological Scenario in String Theory
• The flat limit of three dimensional asymptotically anti-de Sitter spacetimes
• Statistical Entropy of Three-dimensional Kerr-De Sitter Space
• Mechanics of universal horizons
• Some Aspects of the de Sitter/CFT Correspondence
• Hamiltonian analysis of spatially covariant gravity
• On Horava-Lifshitz "Black Holes"
• Towards thermodynamics of universal horizons in Einstein-æther theory
• BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and Statistical Entropy
• Hamiltonian structure of Horava gravity
• Ray tracing Einstein-Æther black holes: Universal versus Killing horizons
• Hawking Radiation of Black Holes in Infrared Modified Hořava-Lifshitz Gravity
• Rotating black holes in three-dimensional Hořava gravity
• Lower-dimensional Horava-Lifshitz gravity
• Consistency of the Hamiltonian formulation of the lowest-order effective action of the complete Horava theory
• Thermodynamics of Exotic Black Holes, Negative Temperature, and Bekenstein-Hawking Entropy
• The Role of Angular Momentum and Cosmic Censorship in the (2+1)-Dimensional Rotating Shell Collapse
• Causality and black holes in spacetimes with a preferred foliation
• Black hole radiation in the presence of a universal horizon
• Killing Horizons: Negative Temperatures and Entropy Super-Additivity
• Can Hawking temperatures be negative ?
• Black hole solutions in Horava-Lifshitz Gravity with cubic terms
• Smeared Hairs and Black Holes in Three-Dimensional de Sitter Spacetime
• BTZ Black Hole with Higher Derivatives, the Second Law of Thermodynamics, and Statistical Entropy: A New Proposal
• Smeared BTZ Black Hole from Space Noncommutativity
• Hawking Radiation from Universal Horizons
• Baby de Sitter Black Holes and dS${}_3$/CFT${}_2$
• Holography in Three-dimensional Kerr-de Sitter Space with a Gravitational Chern-Simons Term
• Fermions Analysis of IR modified Horava-Lifshitz gravity: Tunneling and Perturbation Perspectives
• The Rotating Black Hole in Renormalizable Quantum Gravity: The Three-Dimensional Hořava Gravity Case
• Notes on the Area Theorem
• The point-particle solution and the asymptotic flatness in 2+1 Horava gravity
• The Hamiltonian Dynamics of Horava Gravity
• Complete Classification of Four-Dimensional Black Hole and Membrane Solutions in IR-modified Hořava Gravity