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Flat rotation curves in disk galaxies represent the main evidence for largeamounts of surrounding dark matter. Despite of the difficulty in identifyingthe dark matter contribution to the total mass density in our Galaxy, stellarkinematics, as tracer of gravitational potential, is the most reliableobservable for gauging different matter components. This work tests theflatness of the MW rotation curve with a simple general relativistic modelsuitable to represent the geometry of a disk as a stationary axisymmetric dustmetric at a sufficiently large distance from a central body. Circularvelocities of unprecedented accuracy were derived from the Gaia DR2 data for acarefully selected sample of disk stars. We then fit these velocities to boththe classical, i.e. including a dark matter halo, rotation curve model and arelativistic analogue, as derived form the solution of Einstein's equation. TheGR-compliant MW rotational curve model results statistically indistinguishablefrom its state-of-the-art DM analogue. This supports our ansatz that astationary and axisymmetric galaxy-scale metric could "fill the gap" in abaryons-only Milky Way, suggestive of star orbits dragged along the backgroundgeometry. We confirmed that geometry is a manifestation of gravity according tothe Einstein theory, in particular the weak gravitational effect due to theoff-diagonal term of the metric could mimic for a "DM-like" effect in theobserved flatness of the MW rotation curve. In the context of Local Cosmology,our findings are suggestive of a Galaxy phase-space as the exteriorgravitational field of a Kerr-like source (inner rotating bulge) without theneed of extra-matter.

Testing dark matter and geometry sustained circular velocities in the Milky Way with Gaia DR2