Quantum Black Holes: the Event Horizon as a Fuzzy Sphere

TL;DR

This paper models black hole event horizons as fuzzy spheres, revealing their non-commutative geometry at quantum scales and deriving a quantized mass spectrum based on quantum numbers, with implications for extremal black holes.

Contribution

It introduces a fuzzy sphere model for black hole horizons, deriving a quantum mass spectrum and proposing modifications to classical extremal bounds.

Findings

Event horizon modeled as a fuzzy sphere with non-commutative geometry.

Derived a quantized mass spectrum using four quantum numbers.

Suggested modifications to classical extremal black hole bounds.

Abstract

Modeling the event horizon of a black hole by a fuzzy sphere it is shown that in the classical limit, for large astrophysical black-holes, the event horizon looks locally like a non-commutative plane with non-commutative parameter dictated by the Planck length. Some suggestions in the literature concerning black hole mass spectra are used to derive a formula for the mass spectrum of quantum black holes in terms of four integers which define the area, angular momentum, electric and magnetic charge of the black hole. We also suggest how the classical bounds on extremal black holes might be modified in the quantum theory.