  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.
