Sensing Gravity with Polarized Electromagnetic Radiation

Polarization wiggling is an observational effect of a gravitational field on the polarization of electromagnetic radiation traversing it. We find that in linear gravity, the polarization wiggle rate contributions from scalar, vector and tensor perturbations are independent and gauge invariant. While vector and tensor perturbations do induce polarization wiggling, scalar perturbations do not. 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? 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 rate around the direction of propagation 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. Finally, the polarization wiggling effect induced by a gravitational tensor mode with arbitrary polarization is analyzed. The effect is demonstrated for two cases: 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 of the gravitational tensor mode 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 electromagnetic radiation emitted by multiple sources at known positions from different directions enables all state parameters of a gravitational tensor mode to be determined.