Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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2009-09-15

JHEP 0910:080,2009

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, no figure; v2, a minor error corrected

Scientific paper

10.1088/1126-6708/2009/10/080

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.

**Cai Rong-Gen**

Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics

Scientist

**Liu Yan**

Physics – High Energy Physics – High Energy Physics - Theory

Scientist

**Sun Ya-Wen**

Physics – High Energy Physics – High Energy Physics - Theory

Scientist

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