Quantum Kerr Black Hole from Matrix Theory of Quantum Gravity

Abstract: Recently, a quantum mechanical theory of quantum spaces described by a large $N$ non-commutative coordinates is proposed as a theory 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 of the Kerr black hole. These results provide further support that the proposed theory of quantum spaces is a plausible candidate for the theory of quantum gravity.