The stability of scalar perturbations of a Kerr-metric black hole

Weak perturbations assumed to obey the scalar wave equation EJ = 0 in the exterior of a Kerr-metric black hole are studied. Attention is focused on normal modes, which have timedependences of the form . Analytic and numerical analyses reveal that there are no physically acceptable normal modes that are unstable, i.e., that have frequencies a' in the lower half of the complex plane. Hence there is no indication at this level of approximation that Kerr black holes are unstable. Subject headings: black holes - relativity