A Generalized Uncertainty Principle in Quantum Gravity

TL;DR

This paper derives a generalized uncertainty principle in quantum gravity, suggesting a minimum length scale near the Planck length and redefining black hole concepts at quantum scales.

Contribution

It presents a model-independent derivation of a generalized uncertainty principle consistent with string theory results, highlighting fundamental limits in measuring black hole horizons.

Findings

Minimum length of order Planck length emerges naturally.

Black hole concept becomes undefined below Planck mass.

Generalized uncertainty principle aligns with string theory predictions.

Abstract

We discuss a Gedanken experiment for the measurement of the area of the apparent horizon of a black hole in quantum gravity. Using rather general and model-independent considerations we find a generalized uncertainty principle which agrees with a similar result obtained in the framework of string theories. The result indicates that a minimum length of the order of the Planck length emerges naturally from any quantum theory of gravity, and that the concept of black hole is not operationally defined if the mass is smaller than the Planck mass.