This paper is a sequel to our previous work for accretion onto a Schwarzschild black hole and the so-called standing accretion shock instability; in this paper, we investigate nonaxisymmetric perturbations for a Kerr black hole. The linear and nonlinear phases for the shock evolution are analyzed in detail by both two-dimensional 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 are also evident. Interestingly, the oscillation periods of the fundamental unstable modes are dependent only on the shock radius irrespective of the injection parameters.
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