Perturbations of a rotating black hole. II. Dynamical stability of the Kerr metric

If unstable, a rotating black hole would spontaneously radiate gravitational waves and evolve dynamically to some new (unknown) final state. This paper tests the dynamical stability of rotating holes by numerical integration of the separable perturbation equations for the Kerr metric. No instabilities are found in any of the dozen or so lowest angular modes tested, for any value of specific angular momentum 0 < a < M. Even in the limit a M, the hole appears to be stable. These stability results add credibility to the use of the Kerr metric in detailed astrophysical models. A numerical technique for preserving accuracy on an asymptotically small solution to an ordinary differential equation in the presence of an asymptotically large one is described. Subject headings: black holes - gravitation - relativity - rotation