Wave propagation and quasinormal mode excitation on Schwarzschild spacetime

作者：Dolan Sam R^*; Ottewill Adrian C

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2011, 84(10): 104002.

DOI：10.1103/PhysRevD.84.104002

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

• 出版日期2011-11-2