Controlled regularity at future null infinity from past asymptotic initial data: massless fields

Understand

We study the relationship between asymptotic characteristic initial data at past null infinity and the regularity of solutions at future null infinity for the massless linear spin-s field equations on Minkowski space.

• By quantitatively controlling the solutions on a causal rectangle reaching the conformal boundary, we relate the (generically singular) behaviour of the solutions near past null infinity, future null infinity, and spatial infinity.
• Our analysis uses Friedrich's cylinder at spatial infinity together with a careful Gr\"onwall-type estimate that does not degenerate at the intersection of null infinity and the cylinder (the so-called critical sets).