Linear waves in the Kerr geometry: A mathematical voyage to black hole physics
- 1 January 2009
- journal article
- Published by American Mathematical Society (AMS) in Bulletin of the American Mathematical Society
- Vol. 46 (4), 635
- https://doi.org/10.1090/s0273-0979-09-01258-0
Abstract
This paper gives a survey of wave dynamics in the Kerr space-time geometry, the mathematical model of a rotating black hole in equilibrium. After a brief introduction to the Kerr metric, we review the separability properties of linear wave equations for fields of general spin , corresponding to scalar, Dirac, electromagnetic fields and linearized gravitational waves. We give results on the long-time dynamics of Dirac and scalar waves, including decay rates for massive Dirac fields. For scalar waves, we give a rigorous treatment of superradiance and describe rigorously a mechanism of energy extraction from a rotating black hole. Finally, we discuss the open problem of linear stability of the Kerr metric and present partial results.Keywords
Other Versions
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