Stability of five-dimensional Myers-Perry black holes under massive scalar perturbation: bound states and quasinormal modes

The stability of five-dimensional singly rotating Myers-Perry Black Holes against massive scalar perturbations is studied. Both the quasibound states and quasinormal modes of the massive scalar field are considered. For the quasibound states, we use an analytical method to discuss the effective potential felt by the scalar field, and found that there is no potential well outside the event horizon. Thus, singly rotating Myers-Perry Black Holes are stable against the perturbation of quasibound states of massive scalar fields. Then, We use continued fraction method based on solving a seven-term recurrence relations to compute the spectra of the quasinormal modes. For different values of the black hole rotation parameter $a$, scalar mass parameter $\mu$ and angular quantum numbers, all found quasinormal modes are damped. So singly rotating Myers-Perry Black Holes are also stable against the perturbation of quasinormal modes of massive scalar fields. Besides, when the scalar mass $\mu$ becomes relatively large, the long-living quasiresonances are also found as in other rotating black hole models. Our results complement previous arguments on the stability of five-dimensional singly rotating Myers-Perry black holes against massive scalar perturbations.