Wave Propagation and Quasinormal Mode Excitation on Schwarzschild Spacetime

Understand

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.