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

The tunneling approach beyond the 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 show that the quantity H in the corrected temperature is the explicit function of the only free parameter F (if we apply the change of variables F = hS(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. Copyright (C) EPLA, 2011