A nonlinear Klein-Gordon equation on Kerr metrics

We consider the nonlinear Klein-Gordon equation squareu + m(2)u + lambda\u\(2)u = 0, with lambda greater than or equal to 0, outside a Kerr black hole. We solve the global Cauchy problem for large data with minimum regularity.: Then, using a Penrose compactification, we prove, in the massless case, the existence of smooth asymptotic profiles and Sommerfeld radiation conditions, at the horizon and at null infinity, for smooth solutions. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.