Large-scale optical interferometry in general spacetimes

TL;DR

This paper develops a formalism for calculating frequency shifts of light signals in general curved spacetimes, simplifying analysis of optical interferometry experiments in relativistic settings.

Contribution

It introduces a geometric optics-based method to evaluate frequency shifts without local Lorentz transformations, applicable to various spacetimes including near-Earth environments.

Findings

The formalism generalizes Doppler frequency-shift calculations.

Application to large-scale optical interferometry demonstrates practical utility.

Analysis of phase-shifts in experiments like the optical COW experiment.

Abstract

We introduce a convenient formalism to evaluate the frequency-shift affecting a light signal propagating on a general curved background. Our formulation, which is based on the laws of geometric optics in a general relativistic setting, allows to obtain a transparent generalization of the Doppler frequency-shift without requiring to perform Local Lorentz transformations. It is easily applicable to stationary spacetimes, and in particular to the near-Earth experiments where geometry is described in the parametrized post-Newtonian approximation. We apply our recipe to evaluate the phase-shift arising in large-scale optical interferometric experiments, as the optical version of the Colella-Overhauser-Werner experiment.