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  Caustics and wave propagation in curved spacetimes

Harte, A. I., & Drivas, T. D. (2012). Caustics and wave propagation in curved spacetimes. Physical Review D, 85(12): 124039. doi:10.1103/PhysRevD.85.124039.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-A05C-9 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-A05F-3
Genre: Journal Article

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 Creators:
Harte, Abraham I.1, Author              
Drivas, Theodore D., 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: We investigate the effects of light cone caustics on the propagation of linear scalar fields in generic four-dimensional spacetimes. In particular, we analyze the singular structure of relevant Green functions. As expected from general theorems, Green functions associated with wave equations are globally singular along a large class of null geodesics. Despite this, the "nature" of the singularity on a given geodesic does not necessarily remain fixed. It can change character on encountering caustics of the light cone. These changes are studied by first deriving global Green functions for scalar fields propagating on smooth plane wave spacetimes. We then use Penrose limits to argue that there is a sense in which the "leading order singular behavior" of a (typically unknown) Green function associated with a generic spacetime can always be understood using a (known) Green function associated with an appropriate plane wave spacetime. This correspondence is used to derive a simple rule describing how Green functions change their singular structure near some reference null geodesic. Such changes depend only on the multiplicities of the conjugate points encountered along the reference geodesic. Using sigma(p,p') to denote a suitable generalization of Synge's world function, conjugate points with multiplicity 1 convert Green function singularities involving delta(sigma) into singularities involving 1/pi sigma (and vice-versa). Conjugate points with multiplicity 2 may be viewed as having the effect of two successive passes through conjugate points with multiplicity 1.

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 Dates: 2012-02-022012-05-092012-06-012012
 Publication Status: Published in print
 Pages: 34 pages, 7 figures, added additional figures and explanation
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 Identifiers: arXiv: 1202.0540
DOI: 10.1103/PhysRevD.85.124039
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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : Published for the American Physical Society by the American Institute of Physics
Pages: - Volume / Issue: 85 (12) Sequence Number: 124039 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: https://pure.mpg.de/cone/journals/resource/111088197762258