Topological Black Holes in Horava-Lifshitz Gravity

TL;DR

The paper addresses the thermodynamics of topological black holes in Horava-Lifshitz gravity with horizon curvature $2k$ in the λ=1 sector. It derives the topological solutions, defines a finite mass via a Hamiltonian boundary term, and computes the Hawking temperature and entropy, revealing a logarithmic correction to the area term. A notable result is a duality between the Hawking temperature behaviors of Horava-Lifshitz black holes (for $k=1,0,-1$) and those in Einstein gravity with reversed horizon curvatures, together with thermodynamic stability across cases. The charged extension shows how Maxwell fields modify the solutions, yielding a HL analogue of AdS Reissner-Nordström in the appropriate limit, and confirms the entropy–area relationship with quantum-like corrections. These findings illuminate quantum corrections to black hole thermodynamics in a UV-complete gravity framework and have potential implications for holography and quantum gravity corrections.

Abstract

We find topological (charged) black holes whose horizon has an arbitrary constant scalar curvature $2k$ in Hořava-Lifshitz theory. Without loss of generality, one may take $k=1,0$ and -1. The black hole solution is asymptotically AdS with a nonstandard asymptotic behavior. Using the Hamiltonian approach, we define a finite mass associated with the solution. We discuss the thermodynamics of the topological black holes and find that the black hole entropy has a logarithmic term in addition to an area term. We find a duality in Hawking temperature between topological black holes in Hořava-Lifshitz theory and Einstein's general relativity: the temperature behaviors of black holes with $k=1, 0$ and -1 in Hořava-Lifshitz theory are respectively dual to those of topological black holes with $k=-1, 0$ and 1 in Einstein's general relativity. The topological black holes in Hořava-Lifshitz theory are thermodynamically stable.