A glimpse at the flat-spacetime limit of quantum gravity using the Bekenstein argument in reverse

TL;DR

This paper explores the flat-spacetime limit of quantum gravity by reversing Bekenstein's black hole entropy argument, linking it to quantum gravity theories' dispersion relations and uncertainty principles.

Contribution

It introduces a novel approach by reversing Bekenstein's argument to gain insights into quantum gravity's fundamental relations and corrections.

Findings

Log-area correction informs dispersion relations in Loop Quantum Gravity.

Generalized Uncertainty Principle relates to black hole entropy corrections.

Reversal of Bekenstein's argument offers new perspectives on quantum gravity.

Abstract

An insightful argument for a linear relation between the entropy and the area of a black hole was given by Bekenstein using only the energy-momentum dispersion relation, the uncertainty principle, and some properties of classical black holes. Recent analyses within String Theory and Loop Quantum Gravity describe black-hole entropy in terms of a dominant contribution, which indeed depends linearly on the area, and a leading log-area correction. We argue that, by reversing the Bekenstein argument, the log-area correction can provide insight on the energy-momentum dispersion relation and the uncertainty principle of a quantum-gravity theory. As examples we consider the energy-momentum dispersion relations that recently emerged in the Loop Quantum Gravity literature and the Generalized Uncertainty Principle that is expected to hold in String Theory.