Global properties of the wave equation on non-globally hyperbolic manifolds

Abstract

We introduce a class of four-dimensional Lorentzian manifolds with closed curves of null type or timelike. We investigate some global problems for the wave equation: uniqueness of solution with data on a changing type hypersurface; existence of resonant states; scattering by a violation of the chronology; global Cauchy problem and asymptotic completeness of the wave operators for the chronological but non-causal metrics. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.