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We consider the quasinormal modes, quasibound states and superradiantinstability of a rotating hairy black hole, which possesses a Horndeski hair asdeviation from Kerr black hole, under the perturbation of massive scalar field.With the use of the matrix method, we mainly calculate the eigenfrequenciesrelated to those modes of the perturbation. Under the perturbation of themassless scalar field, the Horndeski hair and spin parameter have significantinfluences on the quasinormal frequency, but its imaginary part is alwaysfinite negative and no unstable mode is found. Under the perturbation of themassive scalar field, we focus on the eigenfrequencies of quasibound states andfind the modes of which the imaginary part of eigenfrequencies is positive,indicating that the black hole undergoes superradiant instability. Then we scanthe parameters and figure out a diagram in the space of Horndeski hair and spinparameters to distinguish the rotating hairy black hole with superradiantinstability from the stable one.

Scalar field perturbation around a rotating hairy black hole: quasinormal modes, quasibound states and superradiant instability