Wave propagation and quasinormal mode excitation on Schwarzschild spacetime
Wave propagation and quasinormal mode excitation on Schwarzschild spacetime
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 function (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.
104002-[14pp]
Dolan, Sam R.
ee9c2137-170a-4942-9655-862a98f389c2
Ottewill, Adrian C.
258dc2c8-31e9-4a5b-be1b-ba6d2abe05d2
2 November 2011
Dolan, Sam R.
ee9c2137-170a-4942-9655-862a98f389c2
Ottewill, Adrian C.
258dc2c8-31e9-4a5b-be1b-ba6d2abe05d2
Dolan, Sam R. and Ottewill, Adrian C.
(2011)
Wave propagation and quasinormal mode excitation on Schwarzschild spacetime.
Physical Review D, 84 (10), .
(doi:10.1103/PhysRevD.84.104002).
Abstract
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 function (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.
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Published date: 2 November 2011
Organisations:
Applied Mathematics
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Local EPrints ID: 202353
URI: http://eprints.soton.ac.uk/id/eprint/202353
ISSN: 1550-7998
PURE UUID: c535fa1d-8b90-47bb-ac88-48061cccb321
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Date deposited: 07 Nov 2011 10:02
Last modified: 14 Mar 2024 04:24
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Author:
Sam R. Dolan
Author:
Adrian C. Ottewill
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