Horizon wave-function for single localized particles: GUP and quantum black hole decay

TL;DR

This paper introduces a horizon wave-function approach to unify quantum mechanics and general relativity, predicting black hole formation probabilities, a minimum black hole mass, an effective GUP, and describing microscopic black hole decay.

Contribution

It presents a novel horizon wave-function framework that combines quantum wave-functions with gravitational effects, leading to new insights on black hole thresholds and decay.

Findings

Probability of black hole formation depends on particle mass

Existence of a minimum black hole mass scale

Decay of microscopic black holes aligns with GUP predictions

Abstract

A localised particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle's energy density exceeds a certain threshold, it should be a black hole. In order to combine these two pictures, we introduce a horizon wave-function determined by the particle wave-function in position space, which eventually yields the probability that the particle is a black hole. The existence of a minimum mass for black holes naturally follows, albeit not in the form of a sharp value around the Planck scale, but rather like a vanishing probability that a particle much lighter than the Planck mass be a black hole. We also show that our construction entails an effective Generalised Uncertainty Principle (GUP), simply obtained by adding the uncertainties coming from the two wave-functions associated to a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts.