Wave propagation and quasinormal mode excitation on Schwarzschild spacetime

Sam R. Dolan and Adrian C. Ottewill
Phys. Rev. D 84, 104002 – Published 2 November 2011; Erratum Phys. Rev. D 84, 109903 (2011)

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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  • Received 8 August 2011
  • Publisher error corrected 10 November 2011

DOI:https://doi.org/10.1103/PhysRevD.84.104002

© 2011 American Physical Society

Corrections

10 November 2011

Erratum

Authors & Affiliations

Sam R. Dolan*

  • School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, UK

Adrian C. Ottewill

  • School of Mathematical Sciences and Complex & Adaptive Systems Laboratory, University College Dublin, Belfield, Dublin 4, Ireland

  • *s.dolan@soton.ac.uk
  • adrian.ottewill@ucd.ie

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Issue

Vol. 84, Iss. 10 — 15 November 2011

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