Quantum Kerr black hole from matrix theory of quantum gravity

Recently, a quantum mechanical theory of quantum spaces described by a large <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>N</a:mi></a:math> non-commutative coordinates is proposed as a model for quantum gravity []. 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.