ar X iv : g r - qc / 0 21 20 35 v 2 1 3 Ja n 20 03 The scalar perturbation of the higher - dimensional rotating black holes .

The massless scalar field in the higher-dimensional Kerr black hole (Myers-Perry solution with a single rotation axis) has been investigated. It has been shown that the field equation is separable in arbitrary dimensions. The quasi-normal modes of the scalar field have been searched in five dimensions using the continued fraction method. The numerical result shows the evidence for the stability of the scalar perturbation of the five-dimensional Kerr black holes. The time scale of the resonant oscillation in the rapidly rotating black hole, in which case the horizon radius becomes small, is characterized by (black hole mass)(Planck mass) rather than the light-crossing time of the horizon.