Wigner phase of photonic helicity states in the spacetime of the Earth

We study relativistic effects on polarised photons that travel in a curved spacetime. As a concrete application, we consider photons in the gravitational field of the Earth, on a closed path that starts at a terrestial laboratory, is reflected at one or more satellites, and finally returns to the laboratory. We find that the photons acquire a non-trivial Wigner phase already when the gravitational field is static, such as the Schwarzschild spacetime, where previous studies have found a trivial Wigner phase for closed photon paths. A gauge-invariant description of this nontrivial Wigner phase remains an open question, to be resolved before the formalism can provide predictions for experiments.