Logarithmic corrections to black hole and black ring entropy in tunneling approach

TL;DR

This paper uses the tunneling approach beyond semiclassical approximation to derive logarithmic corrections to the entropy of black holes and black rings, linking these corrections to the first law of thermodynamics and the corrected temperature.

Contribution

It demonstrates that the leading order logarithmic correction to entropy naturally arises from the corrected temperature and thermodynamics, extending the analysis to black rings.

Findings

Logarithmic correction to black hole entropy confirmed

Application of tunneling approach to black rings shows similar corrections

Corrected temperature explicitly depends on auxiliary parameter 

Abstract

The tunneling approach beyond semiclassical approximation has been used to calculate the corrected Hawking temperature and entropy for various black holes and FRW universe model. We examine their derivations, and prove that the quantity $H$ in the corrected temperature is the explicit function of the only free parameter $\mathcal{A}$ (which is an auxiliary parameter defined by $\mathcal{A}=\hbar S_{BH}$). Our analysis improves previous calculations, and indicates that the leading order logarithmic correction to entropy is a natural result of the corrected temperature and the first law of thermodynamics. Additionally, we apply the tunneling approach beyond semiclassical approximation to neutral black rings. Based on the analysis, we show that the entropy of neutral black rings also has a logarithmic leading order correction.