Bachelot, Alain; Nicolas, Jean-Philippe Nonlinear Klein Gordon equation on Schwarzschild type metric. (Équation non linéaire de Klein-Gordon dans des métriques de type Schwarzschild.) (French) Zbl 0776.35052 C. R. Acad. Sci., Paris, Sér. I 316, No. 10, 1047-1050 (1993). 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. Cited in 4 Documents MSC: 35Q40 PDEs in connection with quantum mechanics 83F05 Relativistic cosmology 53Z05 Applications of differential geometry to physics Keywords:Cauchy problem; nonlinear Klein-Gordon; spherical black hole; impedance condition; Sommerfeld condition PDFBibTeX XMLCite \textit{A. Bachelot} and \textit{J.-P. Nicolas}, C. R. Acad. Sci., Paris, Sér. I 316, No. 10, 1047--1050 (1993; Zbl 0776.35052)