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Quantum Kerr black hole from matrix theory of quantum gravity

Chong-Sun Chu

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Phys. Rev. D 112, 046014 – Published 19 August, 2025

DOI: https://doi.org/10.1103/5rwl-tr4y

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 [arXiv:2406.01466]. 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.

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Phys. Rev. D 112, 046014– Published 19 August, 2025
  • Received 25 June 2024
  • Accepted 30 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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