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A recent analysis of data from the ESA Gaia mission demonstrated that thekinematics of stars in the Milky Way can be modelled without invoking thepresence of dark matter whatsoever. Indeed, the higher-than-Keplerianvelocities observed in outer stars can be ascribed to the properties of thegeneral relativistic (GR) metric assumed to describe the Galaxy. Here wegeneralize the concept, and derive the most general exact GR model for astationary axi-symmetric dynamically cold dust structure.  We explicitly show how deviations from the commonly adopted Newtoniandynamics are indeed manifest even at low velocities and low densities. Weprovide for the first time a detailed description of the frequency shiftexperienced by photons travelling from any emission site within an externaldisc galaxy to the observer, relating the outcome of the shift measurement tothe gravitational properties of the galaxy. Finally, we devise a novel,groundbreaking observational test potentially able to fully characterize the GRmetric under the minimal set of assumptions mentioned above. The proposedexperiment exploits the effects non-diagonal GR terms have on the frequencyshift of photons, ultimately providing a test to evaluate whether dark matteris actually required by disc galaxy kinematics.

Re-weighting dark matter in disc galaxies: a new general relativistic observational test