Asymptotics of scalar waves on long-range asymptotically Minkowski spaces

Abstract

We show the existence of the full compound asymptotics of solutions to the scalar wave equation on long-range non-trapping Lorentzian manifolds modeled on the radial compactification of Minkowski space. In particular, we show that there is a joint asymptotic expansion at null and timelike infinity for forward solutions of the inhomogeneous equation. In two appendices we show how these results apply to certain spacetimes whose null infinity is modeled on that of the Kerr family. In these cases the leading order logarithmic term in our asymptotic expansions at null infinity is shown to be nonzero.

Version 2: 52 pages, 1 figure. Added a remark about Price's law to Section 9.2 and made minor expository changes requested by referee