Eur. Phys. J. C (2010) 68: 255-263
https://doi.org/10.1140/epjc/s10052-010-1344-0

Regular Article - Theoretical Physics

Extremal black holes in the Hořava–Lifshitz gravity

Institute of Basic Science and School of Computer Aided Science, Inje University, Gimhae, 621-749, Korea

^* e-mail: ysmyung@inje.ac.kr

Received: 1 February 2010
Revised: 22 April 2010
Published online: 29 May 2010

Abstract

We study the near-horizon geometry of extremal black holes in the z=3 Hořava–Lifshitz gravity with a flow parameter λ. For λ>1/2, near-horizon geometry of extremal black holes are AdS ₂×S ² with different radii, depending on the (modified) Hořava–Lifshitz gravity. For 1/3≤λ≤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.