Gravitational waves from axions annihilation through quantum field theory

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.