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The No Hair theorem in classical general relativity predicts that rotatingblack holes are specified by the Kerr metric, which is uniquely identified bythe mass and spin. However, as a pioneering study beyond general relativity,the rotating hairy black hole has been proposed, which encompasses the Kerrblack hole as a special case. In these black holes, there are extra hair whichcould appear due to the additional surrounding sources such as dark matter ordark energy. In this work, we study the phenomenology of the rotating hairyblack hole in terms of gravitational perturbations. In particular, thesupperradiance and the quasinormal modes. Using the matching-asymptotic method,we derive the amplification factor and the superradiance conditions. We alsocalculate the quasinormal modes using the continued fraction method. Theresults are in very good agreement with previous studies in the Kerr limit. Wealso show how the amplification and quasinormal modes will shift in response tovariations in the hairy parameters, black hole spin, and quantum numbers.

Superradiance and quasinormal modes of the gravitational perturbation around rotating hairy black hole