  To seek a deeper understanding of wave propagation on the Schwarzschild
spacetime, we investigate the relationship between (i) the lightcone of an
event and its caustics (self-intersections), (ii) the large-$l$ asymptotics of
quasinormal (QN) modes, and (iii) the singular structure of the retarded Green
function (GF) for the scalar field. First, we recall that the GF has a
(partial) representation as a sum over QN modes. Next, we extend a
recently-developed expansion method to obtain asymptotic expressions for QN
wavefunctions and their residues. We employ these asymptotics to show
(approximately) that the QN mode sum is singular on the lightcone, and to
obtain approximations for the GF which are valid close to the lightcone. These
approximations confirm a little-known prediction: the singular part of the GF
undergoes a transition each time the lightcone passes through a caustic,
following a repeating four-fold sequence. We conclude with a discussion of
implications and extensions of this work.
