Gravitational lensing beyond geometric optics: II. Metric independence

Typical applications of gravitational lensing use the properties of electromagnetic or gravitational waves to infer the geometry through which those waves propagate. Nevertheless, the optical fields themselves—as opposed to their interactions with material bodies—encode very little of that geometry:...

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Bibliographic Details
Published in:General relativity and gravitation 2019-12, Vol.51 (12), Article 160
Main Author: Harte, Abraham I.
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Cosmology
Classical and Quantum Gravitation
Configurations
Differential Geometry
Editor’s Choice (Research Article)
Geometrical optics
Gravitational lenses
Gravitational waves
Gravity
Gravity waves
Isomorphism
Mathematical and Computational Physics
Optics
Physics
Physics and Astronomy
Plane waves
Polarization
Quantum Physics
Relativity
Relativity Theory
Spacetime
Theoretical
Wave propagation
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Summary:Typical applications of gravitational lensing use the properties of electromagnetic or gravitational waves to infer the geometry through which those waves propagate. Nevertheless, the optical fields themselves—as opposed to their interactions with material bodies—encode very little of that geometry: it is shown here that any given configuration is compatible with a very large variety of spacetime metrics. For scalar fields in geometric optics, or observables which are not sensitive to the detailed polarization content of electromagnetic or gravitational waves, seven of the ten metric components are essentially irrelevant. With polarization, five components are irrelevant. In the former case, this result together with diffeomorphism invariance allows essentially any geometric-optics configuration associated with a particular spacetime to be embedded into any other spacetime, at least in finite regions. Going beyond the geometric-optics approximation breaks some of this degeneracy, although much remains even then. Overall, high-frequency wave propagation is shown to be insensitive to compositions of certain conformal, Kerr–Schild, and related transformations of the background metric. One application is that new solutions for scalar, electromagnetic, and gravitational waves may be generated from old ones. In one example described here, the high-frequency scattering of a plane wave by a point mass is computed by transforming a plane wave in flat spacetime.
ISSN:0001-7701
1572-9532
DOI:10.1007/s10714-019-2646-7