Sensing Gravity with Polarized Electromagnetic Radiation

Abstract: 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.