A Lifshitz Black Hole in Four Dimensional R^2 Gravity
Abstract
We consider a higher derivative gravity theory in four dimensions with a negative cosmological constant and show that vacuum solutions of both Lifshitz type and Schr\"{o}dinger type with arbitrary dynamical exponent z exist in this system. Then we find an analytic black hole solution which asymptotes to the vacuum Lifshitz solution with z=3/2 at a specific value of the coupling constant. We analyze the thermodynamic behavior of this black hole and find that the black hole has zero entropy while non-zero temperature, which is very similar to the case of BTZ black holes in new massive gravity at a specific coupling. In addition, we find that the three dimensional Lifshitz black hole recently found by E. Ayon-Beato et al. has a negative entropy and mass when the Newton constant is taken to be positive.
Cite
@article{arxiv.0909.2807,
title = {A Lifshitz Black Hole in Four Dimensional R^2 Gravity},
author = {Rong-Gen Cai and Yan Liu and Ya-Wen Sun},
journal= {arXiv preprint arXiv:0909.2807},
year = {2010}
}
Comments
11 pages, no figure; v2, a minor error corrected