Corrections to Bekenstein-Hawking entropy --- Quantum or not-so quantum?

TL;DR

This paper investigates whether black hole entropy corrections indicate quantum or semi-classical degrees of freedom, using dimensional analysis to distinguish their scaling behaviors and implications for quantum gravity theories.

Contribution

It introduces a simple dimensional analysis method to differentiate quantum from semi-classical contributions to black hole entropy corrections.

Findings

Semi-classical entropy shares the same dimensional dependence as the gravity action.

Quantum corrections are expected to have different scaling behavior.

Provides insight into the connection between Einstein's equations and thermodynamics.

Abstract

Hawking radiation and Bekenstein--Hawking entropy are the two robust predictions of a yet unknown quantum theory of gravity. Any theory which fails to reproduce these predictions is certainly incorrect. While several approaches lead to Bekenstein--Hawking entropy, they all lead to different sub-leading corrections. In this article, we ask a question that is relevant for any approach: Using simple techniques, can we know whether an approach contains quantum or semi-classical degrees of freedom? Using naive dimensional analysis, we show that the semi-classical black-hole entropy has the same dimensional dependence as the gravity action. Among others, this provides a plausible explanation for the connection between Einstein's equations and thermodynamic equation of state, and that the quantum corrections should have a different scaling behavior.