Ricci Flow and Circulation Potential: A Model for the Milky Way’s Mass Paradox

Observational data from Gaia DR3 reveals a mass distribution anomaly in the outer Galactic halo (18.5−26.5 kpc), demonstrating a systematic decline in Keplerian mass derived from apparent velocity—a phenomenon defined as "mass inversion". Analysis establishes that observed velocity v_obs, Keplerian velocity v_K, and circulation velocity v_Γ follow a fourth-power relation: v_obs^4=v_K^4+v_Γ^4, with the fit residual accuracy ranging from 4.9% to 0.6%. The circulation potential ΦΓ is characterized as a dynamic non-equilibrium field generated and sustained by spiral arm dynamics. This framework posits that a generalized Ricci flow acts as the dynamical mechanism, which naturally diffuses the spacetime perturbations sourced by the galactic spiral arms outward into the halo, thereby generating and sustaining the conserved gravitational circulation field. The model predicts a Keplerian restoration transition in the 30−35 kpc interval, with the classical Keplerian regime domination beyond 50 kpc, confirming theoretical self-consistency. Future Galactic rotational velocities beyond 26.5 kpc to be revealed by Gaia DR4 will provide a critical test for the theoretical model.