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General Relativity and Gravitation

, Volume 42, Issue 8, pp 1919–1934 | Cite as

Entropy function approach to charged BTZ black hole

  • Yun Soo Myung
  • Yong-Wan Kim
  • Young-Jai Park
Research Article

Abstract

We find solution to the metric function f(r) = 0 of charged BTZ black hole making use of the Lambert function. The condition of extremal charged BTZ black hole is determined by a non-linear relation of M e (Q) = Q 2(1 − ln Q 2). Then, we study the entropy of extremal charged BTZ black hole using the entropy function approach. It is shown that this formalism works with a proper normalization of charge Q for charged BTZ black hole because AdS2 × S1 represents near-horizon geometry of the extremal charged BTZ black hole. Finally, we introduce the Wald’s Noether formalism to reproduce the entropy of the extremal charged BTZ black hole without normalization when using the dilaton gravity approach.

Keywords

Charged BTZ black hole Entropy function approach Wald formalism 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute of Basic Science, School of Computer Aided ScienceInje UniversityGimhaeKorea
  2. 2.Department of Physics, Center for Quantum SpacetimeSogang UniversitySeoulKorea

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