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Departamento de Gravitación y Teoría de CamposSeminarios 2012 |
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Instituto de Ciencias Nucleares, UNAM |
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Departamento de Gravitación y Teoría de CamposSeminarios 2012 |
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Instituto de Ciencias Nucleares, UNAM |
Jueves 1 de marzo, a las 17:00 hrs en la sala de seminarios del ICN
Horst Beyer (MPI for Gravitational Physics, Golm)
On the Stability of the Massive Scalar Field in Kerr Space-Time
| 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 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. Among others, the talk provides an improved bound for this mass above which the solutions of the reduced, by separation in the azimuth angle in Boyer-Lindquist coordinates, Klein-Gordon equation are stable. Finally, it gives new formulations of the reduced equation, in particular, in form of a time-dependent wave equation that is governed by a family of unitarily equivalent positive self-adjoint operators. The latter formulation might turn out useful for further investigation. On the other hand, it is proved that from the abstract properties of this family alone it cannot be concluded that the corresponding solutions are stable. |
