  This paper is a sequel to our previous work for accretion onto a
Schwarzschild black hole and the so-called standing accretion shock instability
(SASI), in this paper we investigate non-axisymmetric perturbations for a Kerr
black hole. The linear and non-linear phases for the shock evolution are
analyzed in detail by both 2D general relativistic hydrodynamical simulations
and linear analysis. Since the structure of steady axisymmetric accretion flows
with a standing shock wave is very sensitive to the inner transonic flow, their
properties such as Mach numbers, which are important for the stability, depend
on the Kerr parameter very much. Although the essential features of the
instability do not differ from the previous results for the Schwarzschild black
hole, the frame dragging effects specific to the Kerr black hole is also
evident. Interestingly, the oscillation periods of the fundamental unstable
modes are dependent only on the shock radius irrespective of the injection
parameters.
