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The first successful detection of gravitational waves (GWs) opened up a new window to study a realm of the most violent phenomena in the universe, such as coalescences of binary black holes (BH–BH), binary neutron stars (NS–NS), and mixed (BH–NS) systems, which are mostly inaccessible in the electromagnetic window. On the other hand, strong gravitational lensing of distant sources, such as galaxies and quasars, by other massive objects lying closer along the line of sight has become a powerful tool in cosmology and astrophysics. With the increasing sensitivity of the new generation of GW detectors, the chances to detect a strongly lensed GW signal are increasing. When GWs are strongly lensed, magnification of the signal intensity is expected, unveiling binary compact objects otherwise too distant to be detected. Such systems are important for their plethora of applications. Lensed GWs can be a test for general relativity, constrain mass distribution in galaxies or galaxy clusters, and provide cosmography information independently of the local cosmic ladders. In this review, we will provide a theoretical background of the gravitational lensing of GWs, including the wave optics regime, which becomes important in this context. Then we will describe the possible cosmological and astrophysical insight hidden in these signals, and present the state-of-the-art searches of lensed GWs in the present and future GW observatories.
Grespan et al. (Sat,) studied this question.