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  Tails of plane wave spacetimes: Wave-wave scattering in general relativity

Harte, A. I. (2013). Tails of plane wave spacetimes: Wave-wave scattering in general relativity. Physical Review D, 88(8): 084059. doi:10.1103/PhysRevD.88.084059.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0014-628A-0 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0015-1188-7
Genre: Journal Article

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 Creators:
Harte, Abraham I.1, Author              
Affiliations:
1Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24013              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
 Abstract: One of the most important characteristics of light in flat spacetime is that it satisfies Huygens' principle: Initial data for the vacuum Maxwell equations evolves sharply along null (and not timelike) geodesics. In flat spacetime, there are no tails which linger behind expanding wavefronts. Tails generically do exist, however, if the background spacetime is curved. The only non-flat vacuum geometries where electromagnetic fields satisfy Huygens' principle are known to be those associated with gravitational plane waves. This paper investigates whether perturbations to the plane wave geometry itself also propagate without tails. First-order perturbations to all locally-constructed curvature scalars are indeed found to satisfy Huygens' principles. Despite this, gravitational tails do exist. Locally, they can only perturb one plane wave spacetime into another plane wave spacetime. A weak localized beam of gravitational radiation passing through an arbitrarily-strong plane wave therefore leaves behind only a slight perturbation to the waveform of the background plane wave. The planar symmetry of that wave cannot be disturbed by any linear tail. These results are obtained by first deriving the retarded Green function for Lorenz-gauge metric perturbations and then analyzing its consequences for generic initial-value problems.

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 Dates: 2013-09-192013
 Publication Status: Published in print
 Pages: 13 pages, 1 figure
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1309.5020
DOI: 10.1103/PhysRevD.88.084059
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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : American Physical Society
Pages: - Volume / Issue: 88 (8) Sequence Number: 084059 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: /journals/resource/111088197762258