Flat rotation curves in disk galaxies represent the main evidence for large amounts of surrounding dark matter. Despite of the difficulty in identifying the dark matter contribution to the total mass density in our Galaxy, stellar kinematics, as tracer of gravitational potential, is the most reliable observable for gauging different matter components. This work tests the flatness of the MW rotation curve with a simple general relativistic model suitable to represent the geometry of a disk as a stationary axisymmetric dust metric at a sufficiently large distance from a central body. Circular velocities of unprecedented accuracy were derived from the Gaia DR2 data for a carefully selected sample of disk stars. We then fit these velocities to both the classical, i.e. including a dark matter halo, rotation curve model and a relativistic analogue, as derived form the solution of Einsteins equation. The GR-compliant MW rotational curve model results statistically indistinguishable from its state-of-the-art DM analogue. This supports our ansatz that a stationary and axisymmetric galaxy-scale metric could fill the gap in a baryons-only Milky Way, suggestive of star orbits dragged along the background geometry. We confirmed that geometry is a manifestation of gravity according to the Einstein theory, in particular the weak gravitational effect due to the off-diagonal term of the metric could mimic for a DM-like effect in the observed flatness of the MW rotation curve. In the context of Local Cosmology, our findings are suggestive of a Galaxy phase-space as the exterior gravitational field of a Kerr-like source (inner rotating bulge) without the need of extra-matter.
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