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

TL;DR

This paper introduces a new thermodynamical entropy for BTZ black holes with higher derivatives, ensuring the second law and matching statistical entropy across all parameter values, resolving previous discrepancies.

Contribution

It proposes a non-negative, consistent entropy definition that aligns thermodynamic and statistical entropies for BTZ black holes with higher curvature and Chern-Simons terms.

Findings

New entropy satisfies the second law and first law of thermodynamics.

Perfect agreement between thermodynamic and statistical entropy for all parameter values.

Resolves previous disagreements in literature regarding entropy calculations.

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.