Near horizon symmetry and entropy of black holes in $f(R)$ gravity and conformal gravity

TL;DR

This paper extends the Noether current method to $f(R)$ and conformal gravity to analyze black hole near horizon symmetries, showing that entropy calculations via Cardy's formula match Wald entropy.

Contribution

It introduces a generalized approach for near horizon symmetry analysis in alternative gravity theories, confirming entropy consistency with Wald's formula.

Findings

Entropy from Cardy's formula matches Wald entropy

Near horizon symmetry analysis applies to $f(R)$ and conformal gravity

Method confirms consistency of entropy calculations in these models

Abstract

We generalize the Noether current method proposed by Majhi and Padmanabhan recently to $f(R)$ gravity and conformal gravity and analyze the near horizon symmetry of black holes in these models. It is shown that the entropy obtained with Cardy's formula agrees with Wald entropy.