Quantum Kerr Black Hole from Matrix Theory of Quantum Gravity

TL;DR

This paper constructs a quantum model of Kerr black holes using non-commutative geometry within a matrix theory framework, successfully reproducing key black hole properties and supporting the model as a quantum gravity candidate.

Contribution

It introduces a rotating noncommutative geometry solution that models Kerr black holes, matching their horizons, entropy, mass, and angular momentum.

Findings

Fuzzy ellipsoid matches Kerr horizon in coordinates

Reproduces Bekenstein-Hawking entropy

Accurately models mass and angular momentum

Abstract

Recently, a quantum mechanical theory of quantum spaces described by a large $N$ non-commutative coordinates is proposed as a model for quantum gravity [1]. In this paper, we construct Kerr black hole as a rotating noncommutative geometry solution of this theory. Due to rotation, the fuzzy sphere is deformed into a fuzzy ellipsoid, which matches exactly the outer horizon of the Kerr black hole in the Boyer-Lindquist coordinates. Together with a half-filled Fermi sea, the fuzzy solution reproduces the Bekenstein-Hawking entropy as well as the mass and angular momentum of the Kerr black hole. These results provide support that the proposed quantum mechanics of quantum spaces as a model of quantum gravity.