Superradiance of rotating black holes surrounded by dark matter

In rotating black hole background surrounded by dark matter, we investigated the super-radiant phenomenon of massive scalar field and its associated instability.Using the method of asymptotic matching, we computed the amplification factor of scalar wave scattering to assess the strength of super-radiance. We discussed the influence of dark matter density on amplification factor in this black hole background. Our result indicates that the presence of dark matter has suppressive influence on black hole super-radiance. We also computed the net extracted energy to further support this result. Finally, we analyzed the super-radiant instability caused by massive scalar field using the black hole bomb mechanism and found that the presence of dark matter has no influence on the super-radiant instability condition.