Entropy function approach to charged BTZ black hole |
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Authors: | Yun Soo Myung Yong-Wan Kim and Young-Jai Park |
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Institution: | 1.Institute of Basic Science, School of Computer Aided Science,Inje University,Gimhae,Korea;2.Department of Physics, Center for Quantum Spacetime,Sogang University,Seoul,Korea |
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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. |
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Keywords: | |
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