  Polarization wiggling is a direct gravitational effect exerted by a
gravitational field on any electromagnetic radiation traversing it. This effect
is investigated in linear gravity for spacetimes with flat or conformally flat
backgrounds. First, we show how the polarization wiggle rates can be computed
in the conformal frame and transformed to the physical frame. Then it is shown
that polarization wiggling is not sensitive to scalar perturbations to the
metric, while vector and tensor perturbations do induce polarization wiggling.
This poses two natural questions: Can polarized electromagnetic radiation be
used to measure vectorial and tensorial components of gravitational fields
directly? And if so, how? Next, polarization wiggling is studied for an
arbitrary vector perturbation to the spacetime metric. In a stationary
spacetime, the polarization wiggle rate is proportional to the difference in
frame dragging rates between radiation emission and measurement events. We show
how this can be used to measure the angular momentum of a gravitational source
if the emitter orbits the gravitational source on a known orbit. Next, the
effect of a gravitational tensor mode with arbitrary polarization is studied.
Finally, the polarization wiggling effect induced by a gravitational tensor
mode is analyzed. Two cases are demonstrated: A spacetime with a flat Minkowski
background and an expanding cosmology with a conformally flat background. In
both cases, the polarization wiggling frequency equals the frequency of the
gravitational tensor mode, while the other state parameters are encoded in the
polarization wiggling amplitude and phase of the polarized radiation. We show
that measurements of polarization wiggling frequency, amplitude and phase of
polarized radiation from different directions enables all state parameters of a
gravitational tensor mode to be determined.
