General Logarithmic Corrections to Bekenstein-Hawking Entropy

TL;DR

This paper derives a general method for calculating quantum logarithmic corrections to black hole entropy, aligning with the generalized uncertainty principle and providing a basis for comparing string theory and loop quantum gravity.

Contribution

It introduces a new approach to compute quantum corrections to Bekenstein-Hawking entropy without uncertainty factors, applicable to various theories.

Findings

Logarithmic correction coefficient matches GUP results

Negative thermal capacity prevents divergence

Method facilitates comparison of quantum gravity theories

Abstract

Recently, there has been a lot of attention devoted to resolving the quantum corrections to the Bekenstein-Hawking entropy of the black hole. In particular, the coefficient of the logarithmic term in the black hole entropy correction has been of great interest. In this paper, the black hole is corresponded to a canonical ensemble in statistics by radiant spectrum, resulted from the black hole tunneling effect studies and the partition function of ensemble is derived. Then the entropy of the black hole is calculated. When the first order approximation is taken into account, the logarithmic term of entropy correction is consistent with the result of the generalized uncertainty principle. In our calculation, there are no uncertainty factors. The prefactor of the logarithmic correction and the one if fluctuation is considered are the same. Our result shows that if the thermal capacity is negative, there is no divergent term. We provide a general method for further discussion on quantum correction to Bekenstein-Hawking entropy. We also offer a theoretical basis for comparing string theory and loop quantum gravitaty and deciding which one is more reliable.