Entropy function approach to charged BTZ black hole

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 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.

18 pages, 8 figures, version to appear in GRG

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Cited by in corpus (8)

• Thermodynamic Geometry Of Charged Rotating BTZ Black Holes
• Thermodynamics of Three-dimensional Black Holes via Charged Particle Absorption
• The Cardy-Verlinde formula and entropy of the charged rotating BTZ black hole
• BPS-like bound and thermodynamics of the charged BTZ black hole
• Asymptotic structure of the Einstein-Maxwell theory on AdS${}_3$
• Thermodynamical and dynamical properties of Charged BTZ Black Holes
• Noncommutative correction to the entropy of charged BTZ black hole
• Conserved charges and black holes in the Einstein-Maxwell theory on AdS${}_3$ reconsidered