Entropy function approach to charged BTZ black hole

Details Entropy function approach to charged BTZ black hole Entropy function approach to charged BTZ black hole

2009-03-12

arxiv.org/abs/0903.2109v2

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 8 figures, version to appear in GRG

Scientific paper

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 AdS_2 x S^1 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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