  We use the scattering method to calculate the gravitational wave from axions
annihilation in the axion cloud formed by the superradiance process around the
Kerr black hole. We consider axions annihilating to gravitons as a three-body
decay process and then calculate the corresponding decay width. In this
approach, we can simply obtain the radiation power of gravitational wave and
give the analytical approximate result with the spin effects of the Kerr black
hole. Our study can also provide a cross-check to the numerical results in the
traditional method.
