Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions

TL;DR

This paper extends the Euclidean gravity framework to compute logarithmic corrections to the entropy of non-extremal black holes across dimensions, carefully treating zero modes and ensemble dependence. By formulating the grand canonical partition function, employing heat-kernel techniques, and analyzing both non-zero and zero-mode contributions, it derives explicit ln a corrections tied to low-energy field content and spacetime dimension. The results yield a universal logarithmic term in microcanonical entropy and reveal both agreements (BTZ) and tensions (Schwarzschild in D=4) with microscopic or loop quantum gravity predictions, providing stringent constraints on ultraviolet completions. The BTZ analysis, in particular, demonstrates consistency between microscopic CFT counts and macroscopic gravity, validating the method in that regime while highlighting ensemble subtleties that affect comparisons with LQG in four dimensions.

Abstract

Euclidean gravity method has been successful in computing logarithmic corrections to extremal black hole entropy in terms of low energy data, and gives results in perfect agreement with the microscopic results in string theory. Motivated by this success we apply Euclidean gravity to compute logarithmic corrections to the entropy of various non-extremal black holes in different dimensions, taking special care of integration over the zero modes and keeping track of the ensemble in which the computation is done. These results provide strong constraint on any ultraviolet completion of the theory if the latter is able to give an independent computation of the entropy of non-extremal black holes from microscopic description. For Schwarzschild black holes in four space-time dimensions the macroscopic result seems to disagree with the existing result in loop quantum gravity.