Horizons and the Wave Function of Planckian Quantum black holes

TL;DR

This paper explores the quantum nature of black holes at the Planck scale, introducing a GUP-based model that predicts a discrete mass spectrum and string-like properties of quantum black holes.

Contribution

It develops a novel GUP framework for Planckian black holes and derives a wave equation revealing a discrete, stable mass spectrum with stringy features.

Findings

Quantum corrections lead to a vanishing Hawking temperature near the Planck mass.

The model predicts a discrete mass spectrum with a stable ground state.

Higher angular momentum states align with Regge trajectories, suggesting string-like behavior.

Abstract

At the Planck scale the distinction between elementary particles and black holes becomes fuzzy. The very definition of a "quantum black hole" (QBH) is an open issue. Starting from the idea that, at the Planck scale, the radius of the event horizon undergoes quantum oscillations, we introduce a black hole mass-radius Generalised Uncertainty Principle (GUP) and derive a corresponding gravitational wavelength. Next we recover a GUP encoding effective geometry. This semi-classical gravitational description admits black hole configurations only for masses higher than the Planck mass. Quantum corrections lead to a vanishing Hawking temperature when the Planck mass is approached from above. Finally we replace our semi-classical model by a relativistic wave equation for the "horizon wave function". The solution admits a discrete mass spectrum which is bounded from below by a stable ground state with energy close to the Planck mass. Interestingly higher angular momentum states fit onto Regge trajectories indicating their stringy nature.