Scattering of Gravitational Waves by the Weak Gravitational Fields of Lens Objects

We consider the scattering of the gravitational waves by the weak gravitational fields of lens objects. We obtain the scattered gravitational waveform by treating the gravitational potential of the lens to first order, i.e. the Born approximation. We find that the effect of scattering on the waveform is roughly given by the Schwartzchild radius of the lens divided by the wavelength of gravitational wave for a compact lens object. If the lens is smoothly distributed, the effect of scattering is of the order of the convergence field κ along the line of sight to the source. In the short wavelength limit, the amplitude is magnified by 1 + κ, which is consistent with the result in weak gravitational lensing. We also derive the correction term due to the effect of finite wavelength.