Generalized Uncertainty Principle and Self-dual Black Holes

TL;DR

This paper explores how the Generalized Uncertainty Principle modifies black hole physics near the Planck scale, proposing a new class of sub-Planckian black holes and connecting quantum mechanics, gravity, and quantum gravity theories.

Contribution

It introduces the concept of a Generalized Event Horizon and suggests the existence of sub-Planckian black holes, linking quantum uncertainty with black hole properties.

Findings

Proposes a transition between Compton wavelength and event horizon size at the Planck scale.

Suggests the existence of sub-Planckian black holes with sizes comparable to their Compton wavelength.

Connects the Generalized Uncertainty Principle with loop quantum gravity results.

Abstract

The Generalized Uncertainty Principle suggests corrections to the Uncertainty Principle as the energy increases towards the Planck value. It provides a natural transition between the expressions for the Compton wavelength below the Planck mass and the black hole event horizon size above this mass. It also suggests corrections to the the event horizon size as the black hole mass falls towards the Planck value, leading to the concept of a Generalized Event Horizon. Extrapolating below the Planck mass suggests the existence of a new class of black holes, whose size is of order the Compton wavelength for their mass. Such sub-Planckian black holes have recently been discovered in the context of loop quantum gravity and it is possible that this applies more generally. This suggests an intriguing connection between black holes, the Uncertainty Principle and quantum gravity.