Polarization distortions of lensed gravitational waves

In general relativity (GR), gravitational waves (GWs) propagate the well-known plus and cross tensorial polarization modes, which are the signature of a massless spin-2 field. However, diffraction of GWs caused by intervening objects along the line of sight can cause the apparent rise of additional polarizations due to GW-curvature interactions. In this paper, we continue the analysis by two of the authors of the present article, on lensing of gravitational waves beyond geometric optics. In particular, we calculate the lensing effect caused by a pointlike lens in the regime where its Schwarzschild radius Rs is much smaller than the wavelength lambda of the signal, itself smaller than the impact parameter b. In this case, the curvature of spacetime induces distortions in the polarization of the wave such that diffraction effects may be misinterpreted as effective scalar and vector polarizations. We find that the amplitude of these apparent nontensor polarizations is suppressed by a factor R-s lambda/b(2) with respect to the amplitude of the tensor modes. We estimate the probability to develop these extra polarization modes for a nearly monochromatic GW in the pulsar timing arrays band traveling through a distribution of galaxies.