Statistical Entropy of BTZ Black Hole in Higher Curvature Gravity

TL;DR

This paper calculates the statistical entropy of the BTZ black hole within higher curvature gravity theories and demonstrates its equivalence to the geometrical entropy, supporting the universality of black hole entropy in various gravity models.

Contribution

It extends the calculation of black hole entropy to higher curvature gravity, showing the consistency between statistical and geometrical approaches in these theories.

Findings

Statistical entropy matches the Noether charge entropy in higher curvature gravity.

The equivalence of geometrical and statistical entropies persists beyond Einstein gravity.

Discusses implications for cosmic censorship and boundary conformal field theories.

Abstract

For the BTZ black hole in the Einstein gravity, a statistical entropy has been calculated to be equal to the Bekenstein-Hawking entropy. In this paper, the statistical entropy of the BTZ black hole in the higher curvature gravity is calculated and shown to be equal to the one derived by using the Noether charge method. This suggests that the equivalence of the geometrical and statistical entropies of the black hole is retained in the general diffeomorphism invariant theories of gravity. A relation between the cosmic censorship conjecture and the unitarity of the conformal field theory on the boundary of AdS is also discussed.