Extremal black holes in the Hořava-Lifshitz gravity

Abstract

We study the near-horizon geometry of extremal black holes in the $z=3$ Hořava-Lifshitz gravity with a flow parameter $\lambda$. For $\lambda >1/2$, near-horizon geometry of extremal black holes are AdS${}_2\times S^2$ with different radii, depending on the (modified) Hořava-Lifshitz gravity. For $1/3\le \lambda \le 1/2$, the radius $v_2$ of $S^2$ is negative, which means that the near-horizon geometry is ill-defined and the corresponding Bekenstein-Hawking entropy is zero. We show explicitly that the entropy function approach does not work for obtaining the Bekenstein-Hawking entropy of extremal black holes.

18 pages, v2:some points on Lifshitz black holes claified, v3: version to appear in EJPC

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