Asymptotics of scalar waves on long-range asymptotically Minkowski spaces

TL;DR

This paper establishes the detailed asymptotic behavior of scalar wave solutions on long-range asymptotically Minkowski spaces, including joint expansions at null and timelike infinity, with applications to Kerr-like spacetimes.

Contribution

It provides the first comprehensive asymptotic expansion results for scalar waves on such non-trapping Lorentzian manifolds, including cases with Kerr null infinity.

Findings

Existence of full asymptotic expansions at null and timelike infinity.

Application of results to Kerr-like spacetimes with nonzero leading logarithmic terms.

Identification of the asymptotic structure of solutions 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.