  It is shown that in the noncommutative spacetime defined by the generalized
Moyal product, consistent noncommutativity can be obtained independent of the
coordinate system such as Cartesian or polar one. In addition, based on the
fact that the generalized Moyal product can be applied to arbitrary spacetime
with non-trivial curvature, the effect of noncommutativity in the axisymmetric
spacetime with central mass is investigated. The results demonstrate how the
noncommutativity of spacetime modify the shape of the stationary limit surface
in the noncommutative Kerr spacetime, which implies that the gravitational
interaction seems to be effectively softened.
