Dolan, S.R. orcid.org/0000-0002-4672-6523 (2018) Geometrical optics for scalar, electromagnetic and gravitational waves on curved spacetime. International Journal of Modern Physics D, 27 (11). 1843010. ISSN 0218-2718
Abstract
The geometrical-optics expansion reduces the problem of solving wave equations to one of the solving transport equations along rays. Here, we consider scalar, electromagnetic and gravitational waves propagating on a curved spacetime in general relativity. We show that each is governed by a wave equation with the same principal part. It follows that: each wave propagates at the speed of light along rays (null generators of hypersurfaces of constant phase); the square of the wave amplitude varies in inverse proportion to the cross-section of the beam; and the polarization is parallel-propagated along the ray (the Skrotskii/Rytov effect). We show that the optical scalars for a beam, and various Newman–Penrose scalars describing a parallel-propagated null tetrad, can be found by solving transport equations in a second-order formulation. Unlike the Sachs equations, this formulation makes it straightforward to find such scalars beyond the first conjugate point of a congruence, where neighboring rays cross, and the scalars diverge. We discuss differential precession across the beam which leads to a modified phase in the geometrical-optics expansion.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 World Scientific Publishing. This is an author produced version of a paper subsequently published in International Journal of Modern Physics D. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Geometrical optics; electromagnetism; gravitational waves; curved spacetime |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 07 Aug 2018 08:47 |
Last Modified: | 20 Aug 2020 12:51 |
Status: | Published |
Publisher: | World Scientific Publishing |
Refereed: | Yes |
Identification Number: | 10.1142/S0218271818430101 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:134203 |