Quasinormal modes, quasibound states, scalar clouds, and superradiant instabilities of a Kerr-like black hole

Abstract: We use the continued fraction method to determine the eigenfrequencies associated with a scalar field around a Kerr-like black hole. The Kerr-like metric considered in this article is a subclass of the general parametrization of axisymmetric black holes proposed by Konoplya, Rezzolla and Zhidenko. In addition to its mass $M$ and specific angular momentum $a$, the black hole depends on a third parameter $\eta$, called the deformation parameter. We investigate how the deformation parameter affects the quasinormal modes and the quasibound states of a massive scalar field around the black hole. In particular, we compute the time scales associated with the superradiant instabilities of the scalar field in such a spacetime. The properties of stationary scalar clouds that could be formed by these instabilities are also discussed.