The Feynman propagator for massive Klein-Gordon fields on radiative asymptotically flat spacetimes

On a large class of asymptotically flat spacetimes which includes radiative perturbations of Minkowski space, we define a distinguished global Feynman propagator for massive Klein-Gordon fields by means of the microlocal approach to non-elliptic Fredholm theory, working in the de,sc-pseudodifferential algebra due to Sussman. We extend the limiting absorption principle (the "iε prescription" for the Feynman propagator) to this setting. Motivated by the complicated Hamilton flow structure arising in this problem, we also prove a new localized radial point estimate in the spirit of Haber-Vasy which, under appropriate nondegeneracy assumptions, allows one to propagate microlocal regularity into a single radial point belonging to a larger radial set which can be a source, sink, or saddle for the Hamilton flow.