Influence of gravitational lensing on gravitational radiation Alexander F. Zakharov * National Astronomical Observatories of CAS, Beijing 100012, China Institute Theoretical and Experimental Physics, 117259 Moscow, Russia Joint Institute for Nuclear Research, 141980 Dubna, Russia Received 1 April 2003; received in revised form 20 November 2006; accepted 21 November 2006 Abstract In a paper by [Wang, Y., Stebbins, A., Turner, E.L. Gravitational lensing of gravitational waves from merging neutron star binaries. Phys. Rev. Lett. 77, 2875–2878, 1996] an influence of gravitational lensing on increasing an estimated rate of gravitational radiation sources was considered. We show that the authors used the geometrical optics approximation model for gravitational lensing and thus they gave an overestimated rate of possible events for possible sources of gravitational radiation for the advanced LIGO detector. We show also that if we would use a more correct model of gravitational lensing, one could conclude that a more strong influence on increas- ing rate of estimated events of gravitational radiation for advanced LIGO detector could give gravitational lenses of galactic masses but not gravitational lenses of stellar masses as [Wang, Y., Stebbins, A., Turner, E.L. Gravitational lensing of gravitational waves from merging neutron star binaries. Phys. Rev. Lett. 77, 2875–2878, 1996] concluded. Ó 2006 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Gravitational lenses; Microlensing; Gravitational radiation; Black holes Gravitational lenses have long and very interesting his- tory (Schneider et al., 1992; Zakharov, 1997) and now it is well known that gravitational bodies act as amplifiers of electromagnetic radiation. If gravitational lens mass is about the solar mass then the separation angle between images is smaller than 10 3 arcseconds thus, it is impossible to resolve the images. Byalko (1970) described the ideas to detect such phenomenon by monitoring the observed lumi- nosities of background stars. Paczynski (1986a) noted also that the effect can be detected by observations of an inten- sity variation of macro-image of a gravitational lensed sys- tem. He also proposed to investigate microlensing by monitoring the light curves of several millions stars in the Large Magellanic Cloud. Thus, it would be possible to detect the dark matter in the Galactic halo (Paczynski, 1986b). The MACHO (Massive Astrophysical Compact Halo Objects) and French EROS (Experience de Recherche d’Objets Sombres) collaborations reported about the dis- covery of first microlensing events (Alcock et al., 1993; Aubourg et al., 1993) and after that several hundred papers about observations of microlensing and its applications were published (Paczynski, 1996; Roulet and Mollerach, 1997; Zakharov and Sazhin, 1998; Zakharov, 2006). Several authors considered gravitational lensing in framework of a strong field approximation (Virbhadra and Ellis, 2000; Kling et al., 2000; Bozza et al., 2001), namely the authors used Schwarzschild black hole metric to generalize the standard gravitational lens approach for the strong gravitational field case. The investigations are very interesting and important from theoretical point of view, however, one should use such gravitational lens mod- el only if the source is located in the vicinity of the line run- ning through the observer and the gravitational lens and the impact parameter is less than few Schwarzschild radii. Under typical astronomical conditions the probability for this source location could be negligible. We would like to remind here that to observe the ordinary gravitational lens effect, the impact parameter should be less than the Einstein–Chwolson radius (which is usually much greater 0273-1177/$30 Ó 2006 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2006.11.026 * Tel.: +7 495 1299759; fax: +7 495 1270833. E-mail address: zakharov@itep.ru www.elsevier.com/locate/asr Advances in Space Research 39 (2007) 219–223