Increase of the Number of Detectable Gravitational Waves Signals due to Gravitational Lensing

TL;DR

This paper investigates how gravitational lensing affects the detection rate of gravitational waves, finding that the increase in detectable signals is negligible across various lens models and conditions.

Contribution

It provides a detailed analysis of gravitational lensing effects on GW detection rates, including model-dependent magnification estimates and the validity of geometrical optics for current and future detectors.

Findings

The increase in detected GW signals due to lensing is negligible.

Geometrical optics is valid for Earth-based detectors and partially for LISA.

The effect varies strongly with lens model but remains minimal.

Abstract

This article deals with the gravitational lensing (GL) of gravitational waves (GW). We compute the increase in the number of detected GW events due to GL. First, we check that geometrical optics is valid for the GW frequency range on which Earth-based detectors are sensitive, and that this is also partially true for what concerns the future space-based interferometer LISA. To infer this result, both the diffraction parameter and a cut-off frequency are computed. Then, the variation in the number of GW signals is estimated in the general case, and applied to some lens models: point mass lens and singular isothermal sphere (SIS profile). An estimation of the magnification factor has also been done for the softened isothermal sphere and for the King profile. The results appear to be strongly model-dependent, but in all cases the increase in the number of detected GW signals is negligible. The use of time delays among images is also investigated.