Polarization distortions of lensed 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 of [1] 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 λ 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 λ /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.

Detecting the Stochastic Gravitational Wave Background from Massive Gravity with Pulsar Timing Arrays

“…where 2 √ 6 h (0) /α 2 = h l , (h (1) + h (−1) )/2α = h x , −i(h (1) − h (−1) )/2α = h y , (h (2) + h (−2) ) = h + and −i(h (1) − h (−1) ) = h × . It is straightforward to show that, up to an overall factor, the five polarization modes we have defined in (5) are equivalent to those defined in [11].…”

“…On the other hand, new physics can also arise in the gravitational sector of our theories, affecting how gravitational waves are generated, how they propagate through spacetime, and opening up the possibility of the production of entirely new polarization states. Indeed, work has already been carried out exploring the impact of different polarization modes in PTA gravitational wave searches [1].…”

“…metric perturbation around flat spacetime can be expressed in matrix form as, (0)|k| 2m h (1) + h (−1) −i |k| 2m h (1) − h (−1) − (0) |k| 2m h (1) + h (−1) h (2) + h (−2) + (0) −i h (2) − h (−2) k 0 2m h (1) + h (−1) −i |k| 2m h (1) − h (−1) −i h (2) − h (−2) − h (2) + h (−2) + (0) −i k 0 2m h (1) − h (−1) …”