BTZ Black Hole with Higher Derivatives, the Second Law of Thermodynamics, and Statistical Entropy: A New Proposal

Abstract

I consider the thermodynamics of the BTZ black hole in the presence of the higher curvature and gravitational Chern-Simons terms, and its statistical entropy. I propose a new thermodynamical entropy, which being {\it non-negative} manifestly, such as the second law, as well as the first law, of thermodynamics is satisfied. I show that the new \therl entropy agrees perfectly with the statistical entropy for $all$ the values of the conformal factor of the higher curvature terms and the coupling constant of the gravitational Chern-Simons term, in contrast to some disagreements in the literatures. The agreement with both the higher curvature and gravitational Chern-Simons terms is possible because of an appropriate balancing of them, though it is not a trivial matter because of a conflict in the appropriate Hilbert space for a well-defined conformal field theory for each term.

Footnote 8 is rewritten, typos corrected, references updated, accpeted in PRD

References in corpus (5)

• BTZ Black Hole with Chern-Simons and Higher Derivative Terms
• BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and Statistical Entropy
• Thermodynamics of Exotic Black Holes, Negative Temperature, and Bekenstein-Hawking Entropy
• Can Hawking temperatures be negative ?
• Notes on the Area Theorem

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• Galilean Conformal Algebra in Two Dimensions and Cosmological Topologically Massive Gravity
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• Enhanced Asymptotic Symmetry Algebra of 2+1 Dimensional Flat Space
• (2+1)-dimensional solutions in $F(R)$ gravity
• Rotating Black Holes in Three-Dimensional Horava Gravity Revisited