Gravitational lensing beyond geometric optics: I. Formalism and observables

TL;DR

This paper develops a formalism for gravitational lensing that extends beyond geometric optics, accounting for finite-frequency effects on wave propagation, energy, momentum, and observable directions in curved spacetimes.

Contribution

It introduces a comprehensive framework for analyzing wave propagation beyond geometric optics, including finite-frequency corrections to conservation laws and observables in curved spacetime.

Findings

Different components of high-frequency fields scale with distinct powers of frequency.

Finite-frequency corrections affect energy, momentum, and propagation direction observables.

The formalism applies to scalar, electromagnetic, and gravitational waves in generic curved spacetimes.

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."