Polarization distortions of lensed gravitational waves. (arXiv:2104.10119v2 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Dalang_C/0/1/0/all/0/1">Charles Dalang</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Cusin_G/0/1/0/all/0/1">Giulia Cusin</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Lagos_M/0/1/0/all/0/1">Macarena Lagos</a>
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
$R_slambda/b^2$ 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.
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
$R_slambda/b^2$ 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.
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