Gravitational lensing beyond geometric optics: I. Formalism and observables

Abraham I. Harte

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Gravitational lensing beyond geometric optics: I. Formalism and observables

Abraham I. Harte

General Relativity and Quantum Cosmology · Submitted 19 Aug 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The laws of geometric optics and their corrections are derived for scalar, electromagnetic, and gravitational waves propagating in generic curved spacetimes.

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.10 · mentions code or data availability 0.01.

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The laws of geometric optics and their corrections are derived for scalar, electromagnetic, and gravitational waves propagating in generic curved spacetimes. Local peeling-type results are obtained, where different components of high-frequency fields are shown to scale with different powers of their frequencies. Additionally, finite-frequency corrections are identified for a number of conservation laws and observables. Among these observables are a field's energy and momentum densities, as well as several candidates for its corrected "propagation directions."

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The laws of geometric optics and their corrections are derived for scalar, electromagnetic, and gravitational waves propagating in generic curved spacetimes.	contribution 0.95	0.86	0.21	asserted 1.00
s1	Local peeling-type results are obtained, where different components of high-frequency fields are shown to scale with different powers of their frequencies.	result 0.97	0.90	0.14	asserted 1.00
s2	Additionally, finite-frequency corrections are identified for a number of conservation laws and observables.	result 0.79	0.90	0.16	asserted 1.00
s3	Among these observables are a field's energy and momentum densities, as well as several candidates for its corrected "propagation directions."	result 0.82	0.82	0.10	asserted 0.73

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Original abstract

The laws of geometric optics and their corrections are derived for scalar, electromagnetic, and gravitational waves propagating in generic curved spacetimes. Local peeling-type results are obtained, where different components of high-frequency fields are shown to scale with different powers of their frequencies. Additionally, finite-frequency corrections are identified for a number of conservation laws and observables. Among these observables are a field's energy and momentum densities, as well as several candidates for its corrected "propagation directions."

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References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Strong-Field Gravitational-Wave Lensing from Ray-Traced Arrival-Time Surfaces
gr-qc 2026-10 accept novelty 7.0 of 10

A ray-traced arrival-time surface formalism enables wave-optics lensing calculations for sources deep in the strong gravitational field of a Schwarzschild black hole, validated against relativistic scattering and poin...
Scalar and tensor gravitational waves
gr-qc 2020-09 conditional novelty 7.0 of 10

In reduced Horndeski theories, luminal and quasiluminal scalar waves decouple from tensor gravitational waves, while subluminal co-propagating scalar-tensor interactions are suppressed by phase incoherence.
Binary-lens amplification of starlight: from magnification flares to quasi-periodic tracking of orbital evolution
astro-ph.GA 2026-10 conditional novelty 6.0 of 10

Gravitational lensing by supermassive black hole binaries produces a zoo of stellar flares and quasi-periodic signals whose peak shapes, spacings, and Fourier spectra encode the binary's period, eccentricity, inclinat...
Spin precession in the strong deflection limit
gr-qc 2026-07 conditional novelty 6.0 of 10

Spin precession near black holes diverges logarithmically in the strong-deflection limit and is related to the deflection angle by a compact formula.
Gravitational wave lensing as a probe of halo properties and dark matter
astro-ph.CO 2022-12 conditional novelty 5.0 of 10

Wave-optics distortions of lensed gravitational waves can, in Fisher forecasts, pin down a lens's projected mass, impact parameter and inner density slope or core size, opening a route to probing dark matter halo cores.

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14 arXiv papers cite this in 21 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 17 sentences without a confident label

Cites it as background 4 papers

On the other hand, there are studies of GW lensing beyond geometric optics that do not neglect the spin-2 nature of the wave, either introducing a perturbative approach [ref] or importing quantum scattering techniques, see Refs. [ref] for a review and [ref] for a more recent work on the subject.

Wave optics lensing of gravitational waves: theory and phenomenology of triple systems in the LISA band · Introduction · 0.81
In the high-frequency limit the propagation of waves, which is almost always applicable in astrophysical situations, can be well approximated by propagation along null geodesics [ref] .

Bilocal geodesic operators as a tool of investigating the optical properties of spacetimes · Notations and their meanings · 0.86
See Refs. [ref] for recent attempts to model GWs beyond the geometric-optics regime.

Horndeski gravity and standard sirens · Nature of the approximation · 0.91

What it cites · 4 sentences without a confident label

Builds on 1 paper

While these scalars have been computed before for high-frequency circularly-polarized fields [ref] , here we allow for arbitrary polarizations and also state a kind of peeling result which summarizes how the scalars depend on $ω$.

Higher-order geometrical optics for electromagnetic waves on a curved spacetime · Newman-Penrose scalars and peeling · 0.93

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