On the stability of the scalar field in the gravitational field of a rotating (Kerr‐) black hole Free

The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting in this connection is the problem of the stability of the solutions of the Klein‐Gordon equation, describing the propagation of a scalar field in the background of a rotating (Kerr‐) black hole. Results suggest that the stability of the field depends crucially on its mass. The paper presents the status of the research in this area. This includes new rigorous results by the author, in particular, an improved bound for the mass of the field above which the solutions of the reduced, by separation in the azimuth angle in Boyer‐Lindquist coordinates, Klein‐Gordon equation are stable.