Polarization distortions of lensed gravitational waves

TL;DR

This paper investigates how gravitational lensing beyond geometric optics can induce apparent scalar and vector polarization modes in gravitational waves, which are normally only tensor modes in general relativity, especially relevant for pulsar timing array observations.

Contribution

It provides a detailed calculation of polarization distortions caused by small Schwarzschild radius lenses in the wave regime, extending previous geometric optics analyses.

Findings

Apparent non-GR polarizations are suppressed by a factor of R_sλ/b^2.

The probability of observing these extra polarizations in PTA band is estimated.

Lensing can induce effective scalar and vector polarizations in gravitational waves.

Abstract

In general relativity (GR), gravitational waves (GWs) propagate the well-known plus and cross 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 point-like lens, in the regime where its Schwarzschild radius $R_s$ 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 effective scalar and vector polarizations may appear. We find that the amplitude of these apparent non-GR polarizations is suppressed by a factor $R_s\lambda/b^2$ with respect to the amplitude of the GR-like 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.