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
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Revised: 22 April 2010
Published online: 29 May 2010
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.
© Springer-Verlag / Società Italiana di Fisica, 2010