Galaxy Rotation Curves from Curvature anomalies?

Mass curves spacetime, and curved spacetime tells mass how to move (Wheeler. Journey into Gravity & Spacetime). Thus, when one witnesses an anomalous movement of matter (e.g., Galactic Rotation Curves), one is witnessing an anomalous curvature of spacetime, not an anomalous matter distribution directly. Therefore, is it possible to explain Galactic Rotation Curves, without invoking 'Dark Matter', so much as 'Dark Curvature' ???

Simply as a suggestion, if our Cosmos is closed, and if under-dense, evacuated, voids 'poof outward', wouldn't that extra 'outward swelling' of the spacetime, of voids surrounding some mass concentration (e.g. galactic group), impose a 'pinching off' effect, on the throat of the gravity well, of that mass concentration, thereby increasing the curvature, and the sensation of gravity???