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Linear waves in the Kerr geometry: a mathematical voyage to black hole physics. (English) Zbl 1177.83082

Summary: 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 \( s=0,\frac{1}{2}, 1, 2\), 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.

MSC:

83C57 Black holes
35L15 Initial value problems for second-order hyperbolic equations
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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