Topological Black Holes in Horava-Lifshitz Gravity

TL;DR

This paper discovers topological black hole solutions in Hořava-Lifshitz gravity, analyzes their thermodynamics, and reveals a temperature duality with black holes in Einstein's general relativity.

Contribution

It introduces new topological black hole solutions in Hořava-Lifshitz gravity and explores their thermodynamic properties and dualities with Einstein gravity.

Findings

Black hole solutions with arbitrary scalar curvature horizon in Hořava-Lifshitz gravity.

Black hole entropy includes a logarithmic correction to the area law.

Thermodynamically stable black holes with a temperature duality to Einstein gravity.

Abstract

We find topological (charged) black holes whose horizon has an arbitrary constant scalar curvature $2k$ in Ho\v{r}ava-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 Ho\v{r}ava-Lifshitz theory and Einstein's general relativity: the temperature behaviors of black holes with $k=1, 0$ and -1 in Ho\v{r}ava-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 Ho\v{r}ava-Lifshitz theory are thermodynamically stable.