Affiliation:
1. Consortium for Fundamental Physics, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
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.
Funder
Engineering and Physical Sciences Research Council
Science and Technology Facilities Council
Publisher
World Scientific Pub Co Pte Lt
Subject
Space and Planetary Science,Astronomy and Astrophysics,Mathematical Physics
Cited by
15 articles.
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