Dynamically self-regular quantum harmonic black holes

TL;DR

This paper introduces a model of self-regular quantum black holes with a minimal size, using a Bohr-like quantization scheme, supporting the UV self-complete quantum gravity idea and proposing a quantum hoop conjecture.

Contribution

It presents a novel quantum black hole model with a minimal length and a harmonic oscillator energy spectrum, without requiring full quantum gravity details.

Findings

Black holes have a minimal extremal size acting as a short-distance cutoff.

The quantum spectrum of black holes resembles that of a harmonic oscillator.

A quantum hoop conjecture is formulated, supporting the existence of quantum black holes.

Abstract

The recently proposed UV self-complete quantum gravity program is a new and very interesting way to envision Planckian/trans-Planckian physics. in this new framework, high energy scattering is dominated by the creation of micro black holes, and it is experimentally impossible to probe distances shorter than the horizon radius. In this letter we present a model which realizes this idea through the creation of self-regular quantum black holes admitting a minimal size extremal configuration. Their radius provides a dynamically generated minimal length acting as a universal short-distance cut-off. We propose a quantisation scheme for this new kind of microscopic objects based on a Bohr-like approach, which does not require a detailed knowledge of quantum gravity. The resulting black hole quantum picture resembles the energy spectrum of a quantum harmonic oscillator. The mass of the extremal configuration plays the role of zero-point energy. Large quantum number re-establish the classical black hole description. Finally, we also formulate a "quantum hoop conjecture" which is satisfied by all the mass eigen-states and sustains the existence of quantum black holes sourced by Gaussian matter distributions.