Lensing of gravitational waves: universal signatures in the beating pattern

TL;DR

This paper investigates gravitational lensing effects on gravitational waves, revealing universal signatures in beating patterns near caustics and proposing a formula to relate lens mass to interference fringes.

Contribution

It introduces a comprehensive analysis of wave-optics to geometrical optics transition in gravitational lensing, including a new parameter for accurate modeling near caustics.

Findings

Nodal and antinodal lines follow hyperbolas near caustics.

A simple formula relates Fresnel number and source position for geometrical-optics onset.

Lens mass can be inferred from interference fringes.

Abstract

When gravitational waves propagate near massive objects, their paths curve resulting in gravitational lensing, which is expected to be a promising new instrument in astrophysics. If the time delay between different paths is comparable with the wave period, lensing may induce beating patterns in the waveform, and it is very close to caustics that these effects are likely to be observable. Near the caustic, however, the short-wave asymptotics associated with the geometrical optics approximation breaks down. In order to describe properly the crossover from wave optics to geometrical optics regimes, along with the Fresnel number, which is the ratio between the Schwarzschild diameter of the lens and the wavelength, one has to include another parameter - namely, the angular position of the source with respect to the caustic. By considering the point mass lens model, we show that in the two-dimensional parameter space, the nodal and antinodal lines for the transmission factor closely follow hyperbolas in a wide range of values near the caustic. This allows us to suggest a simple formula for the onset of geometrical-optics oscillations which relates the Fresnel number with the angular position of the source in units of the Einstein angle. We find that the mass of the lens can be inferred from the analysis of the interference fringes of a specific lensed waveform.