Corrected entropy of the rotating black hole solution of the new massive gravity using the tunneling method and Cardy formula

TL;DR

This paper investigates the thermodynamics of rotating AdS black holes in three-dimensional massive gravity, calculating corrected temperature and entropy using the tunneling method and Cardy formula, and comparing these approaches.

Contribution

It introduces a method to determine the unknown correction parameter in the tunneling approach by comparing it with the Cardy formula for black hole entropy.

Findings

Corrected temperature and entropy are computed for the black hole.

Comparison of methods helps identify the correction parameter.

Results enhance understanding of black hole thermodynamics in massive gravity.

Abstract

We study the AdS rotating black hole solution for the Bergshoeff-Hohm-Townsend (BHT) massive gravity in three dimensions. The field equations of the asymptotically AdS black hole of the static metric can be expressed as the first law of thermodynamics, i.e. $dE=TdS-PdV$. The corrected Hawking-like temperature and entropy of asymptotically AdS rotating black hole are calculated using the Cardy formula and the tunneling method. Comparison of these methods will help identify the unknown leading correction parameter $\beta_1$ in the tunneling method.