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Nonlinear Klein Gordon equation on Schwarzschild type metric. (Équation non linéaire de Klein-Gordon dans des métriques de type Schwarzschild.) (French) Zbl 0776.35052

Summary: We solve the global Cauchy problem for the nonlinear Klein-Gordon equation outside a spherical black hole. On the black hole horizon the field satisfies the impedance condition of T. Damour. If the space time is asymptotically flat, the massless fields satisfy the Sommerfeld condition at infinity.

MSC:

35Q40 PDEs in connection with quantum mechanics
83F05 Relativistic cosmology
53Z05 Applications of differential geometry to physics
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