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 Schrödinger 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. © 2009 SISSA.
CITATION STYLE
Cai, R. G., Liu, Y., & Sun, Y. W. (2009). A Lifshitz black hole in four dimensional R 2 gravity. Journal of High Energy Physics, 2009(10). https://doi.org/10.1088/1126-6708/2009/10/080
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