When conceptual worlds collide: The GUP and the BH entropy

TL;DR

This paper uses the generalized uncertainty principle to derive quantum corrections to black hole entropy, providing a unified framework that relates the logarithmic correction coefficient to fundamental theory parameters.

Contribution

It introduces a method to determine the coefficient of the logarithmic correction in black hole entropy using GUP, linking it to fundamental theory parameters.

Findings

Quantum-corrected entropy expressed as an expansion consistent with previous results.

Logarithmic correction coefficient linked to a single fundamental parameter.

GUP reduces to Heisenberg uncertainty in weak gravity, extends beyond in strong gravity.

Abstract

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein--Hawking (black hole) entropy. In particular, many researchers have expressed a vested interest in fixing the coefficient of the sub-leading logarithmic term. In the current paper, we are able to make some substantial progress in this direction by utilizing the generalized uncertainty principle (GUP). Notably, the GUP reduces to the conventional Heisenberg relation in situations of weak gravity but transcends it when gravitational effects can no longer be ignored. Ultimately, we formulate the quantum-corrected entropy in terms of an expansion that is consistent with all previous findings. Moreover, we demonstrate that the logarithmic prefactor (indeed, any coefficient of the expansion) can be expressed in terms of a single parameter that should be determinable via the fundamental theory.