# Gravitational lensing beyond geometric optics: I. Formalism and observables

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## 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”.

## Keywords

Wave propagation Gravitational lensing Gravitational waves Geometric optics## Notes

### Acknowledgements

I thank Yi-Zen Chu, Sam Dolan, and Justin Vines for valuable discussions.

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