Gravitational wave propagation beyond geometric optics

TL;DR

This paper investigates gravitational wave lensing beyond the geometric optics approximation, revealing diffraction effects that induce polarization mode mixing and affect the energy distribution of gravitational waves.

Contribution

It introduces a perturbative method to compute corrections beyond geometric optics in gravitational wave lensing, including polarization and energy tensor effects.

Findings

Diffraction causes polarization plane smearing.

Apparent vector and scalar polarization modes emerge.

Diffraction impacts the gravitational wave energy tensor.

Abstract

It is standard practice to study the lensing of gravitational waves (GW) using the geometric optics regime. However, in many astrophysical configurations this regime breaks down as the wavelength becomes comparable to the Schwarzschild radius of the lens. We revisit the lensing of GW including corrections beyond geometric optics. We propose a perturbative method for calculating these corrections simply solving first order decoupled differential equations. We study the behavior of a single ray and find that the polarization plane defined in geometric optics is smeared due to diffraction effects, which leads to the rise of apparent vector and scalar polarization modes. We analyze how these modes depend on the observer choice, and we study the impact of diffraction on the pseudo-stress energy momentum tensor of the gravitational field.