Point-like sources and the scale of quantum gravity

TL;DR

This paper explores how a generalized uncertainty principle with a minimum length scale affects the energy of point-like particles in quantum gravity, suggesting finite energy and implications for black hole evaporation.

Contribution

It demonstrates that incorporating a minimum length scale modifies the classical energy behavior of point-like particles, linking quantum gravity effects to the Equivalence Principle.

Findings

Total energy remains finite for all particle masses.

Minimum length scale prevents classical divergence of energy.

Implications for black hole evaporation stages.

Abstract

We review the General Relativistic model of a (quasi) point-like particle represented by a massive shell of neutral matter which has vanishing total energy in the small-volume limit. We then show that, by assuming a Generalised Uncertainty Principle, which implies the existence of a minimum length of the order of the Planck scale, the total energy instead remains finite and equal to the shell's proper mass both for very heavy and very light particles. This suggests that the quantum structure of space-time might be related to the classical Equivalence Principle and possible implications for the late stage of evaporating black holes are briefly mentioned.