Severe constraints on Loop-Quantum-Gravity energy-momentum dispersion relation from black-hole area-entropy law

TL;DR

This paper investigates the relationship between black-hole entropy and energy-momentum dispersion in Loop Quantum Gravity, concluding that certain linear dispersion relations are incompatible with the black-hole area-entropy law.

Contribution

It reveals that linear dispersion relations in Loop Quantum Gravity are constrained by the black-hole area-entropy law, providing new bounds on quantum gravity models.

Findings

Linear dispersion relations are incompatible with the black-hole entropy law.

Black-hole entropy in Loop Quantum Gravity depends linearly on the area with small corrections.

Certain linear terms in dispersion relations would require entropy contributions proportional to the square root of the area.

Abstract

We explore a possible connection between two aspects of Loop Quantum Gravity which have been extensively studied in the recent literature: the black-hole area-entropy law and the energy-momentum dispersion relation. We observe that the original Bekenstein argument for the area-entropy law implicitly requires information on the energy-momentum dispersion relation. Recent results show that in first approximation black-hole entropy in Loop Quantum Gravity depends linearly on the area, with small correction terms which have logarithmic or inverse-power dependence on the area. Preliminary studies of the Loop-Quantum-Gravity dispersion relation reported some evidence of the presence of terms that depend linearly on the Planck length, but we observe that this possibility is excluded since it would require, for consistency, a contribution to black-hole entropy going like the square root of the area.