Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-09-04
Phys.Rev.D77:126012,2008
Physics
High Energy Physics
High Energy Physics - Theory
Footnote 8 is rewritten, typos corrected, references updated, accpeted in PRD
Scientific paper
10.1103/PhysRevD.77.126012
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.
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