Black Hole in Higher Curvature Gravity and AdS/CFT Correspondence

TL;DR

This paper calculates the classical central charge in higher curvature 3D gravity, derives the BTZ black hole entropy via Cardy's formula, and finds it matches the Iyer-Wald entropy, supporting a generalized AdS/CFT correspondence.

Contribution

It introduces a method to compute the central charge in higher curvature gravity and confirms the consistency of entropy calculations, extending the AdS/CFT correspondence.

Findings

Central charge computed using Legendre transformation.

BTZ black hole entropy matches Iyer-Wald formula.

Supports generalized AdS/CFT correspondence.

Abstract

The classical central charge for the higher curvature gravity in 3-dimensions is calculated using the Legendre transformation method. The statistical entropy of BTZ black hole is derived by the Cardy's formula and the result completely coincides with the Iyer-Wald formula for the geometrical entropy. This coincidence suggests the generalized AdS/CFT correspondence.