The entropy formula of black holes in Minimal Massive Gravity and its application for BTZ black holes

TL;DR

This paper derives a modified black hole entropy formula in Minimal Massive Gravity, applies it to BTZ black holes, and confirms consistency with the dual CFT via the Cardy formula.

Contribution

It introduces a new entropy formula for black holes in MMG, accounting for Chern-Simons and additional terms, and demonstrates its agreement with boundary CFT predictions.

Findings

Modified entropy includes contributions from Chern-Simons and MMG-specific terms.

The entropy formula matches the Cardy formula for the dual CFT.

New term in MMG affects the outer horizon radius contribution.

Abstract

In this paper we obtain the entropy formula of black hole solutions of Minimal Massive Gravity (MMG) by Tachikawa method \cite{a}. Then we apply this formula for BTZ black hole solution. We find that the usual Bekenstein-Hawking entropy is modified. The modification come from Chern-Simons (CS) term and new term in MMG. The contribution of CS term, which is proportional with inner radius of horizon is not new, but last term which is due to the new term of MMG, as usual is proportional to the outer radius of horizon and is new result. Then we show that the total entropy exactly can be reproduced by Cardy formula for entropy of the dual boundary CFT.