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

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. Keyword(s): gravitational waves; gravitational lensing; interferometric detectors of gravitational waves. Dipartimento di Fisica E.R. Caianiello, Universitá di Salerno 84081 Baronissi (Sa), Italy and LERMA/ERGA, Université Paris VI, 4 pl.Jussieu 75005 Paris, France. email: [email protected] or [email protected] LERMA/ERGA, Université Paris VI, 4 pl. Jussieu 75005 Paris, France. e-mail: [email protected] LERMA/ERGA, Université Paris VI, 4 pl. Jussieu 75005 Paris, France. email:[email protected]