# Gravitational lensing of gravitational waves: wave nature and prospects for detection

## TL;DR

This paper explores the gravitational lensing effects on gravitational waves, emphasizing wave phenomena, micro-lensing, and their implications for detection, source localization, and constraining lens properties.

## Contribution

It provides a detailed analysis of wave effects in gravitational lensing of gravitational waves and discusses the observational challenges and potential uses of micro-lensing in astrophysics.

## Key findings

- Micro-lensing combined with strong lensing causes detectable phase shifts.
- Wave effects are significant for low SNR detections of extragalactic sources.
- Micro-lensing probability is high for sources in the galactic plane.

## Abstract

We discuss the gravitational lensing of gravitational wave signals from coalescing binaries. We delineate the regime where wave effects are significant from the regime where geometric limit can be used. Further, we focus on the effect of micro-lensing and the combined effect of strong lensing and micro-lensing. We find that micro-lensing combined with strong lensing can introduce time varying phase shift in the signal and hence can lead to detectable differences in the signal observed for different images produced by strong lensing. This, coupled with the coarse localization of signal source in the sky for gravitational wave detections, can make it difficult to identify the common origin of signal corresponding to different images and use observables like time delay. In case we can reliably identify corresponding images, micro-lensing of individual images can be used as a tool to constrain properties of micro-lenses. Sources of gravitational waves can undergo microlensing due to lenses in the disk/halo of the Galaxy, or due to lenses in an intervening galaxy even in absence of strong lensing. In general the probability for this is small with one exception: Extragalactic sources of gravitational waves that lie in the galactic plane are highly likely to be micro-lensed. Wave effects are extremely important for such cases. In case of detections of such sources with low SNR, the uncertainty of occurrence of microlensing or otherwise introduces an additional uncertainty in the parameters of the source.