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Wave propagation and quasinormal mode excitation on Schwarzschild spacetime

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.
1550-7998
104002-[14pp]
Dolan, Sam R.
ee9c2137-170a-4942-9655-862a98f389c2
Ottewill, Adrian C.
258dc2c8-31e9-4a5b-be1b-ba6d2abe05d2
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), 104002-[14pp]. (doi:10.1103/PhysRevD.84.104002).

Record type: Article

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

Identifiers

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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Contributors

Author: Sam R. Dolan
Author: Adrian C. Ottewill

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