What question did this study set out to answer?

The research aims to explain the phenomenon of flat rotation curves in galaxies without relying on dark matter.

June 26, 2026Open Access

Vortex Dynamics: Geometric Origin of Flat Rotation Curves

Key Points

The research aims to explain the phenomenon of flat rotation curves in galaxies without relying on dark matter.
Introduced the Vortex Dynamics framework based on unique spacetime geometry around galaxies.
Derived key relations such as flat rotation curves and the Baryonic Tully-Fisher Relation from gravitational potential modifications.
Compared predictions with Milky Way and SPARC galaxy rotation curves, achieving high accuracy.
Flat rotation curves were derived, reducing χ2 by 5× compared to Newtonian predictions.
Matched galaxy rotation data to an accuracy of less than 3% using only baryonic mass.
Eliminated the need for dark matter at galactic scales.

Abstract

Galactic rotation curves remain flat at radii where Newtonian gravity predictsKeplerian decline. Dark matter halos and MOND have been proposed to resolvethis tension. I introduce Vortex Dynamics, a framework in which spacetime aroundgalaxies possesses a Gabriel’s Horn / Torricelli’s Trumpet-like geometry induced byframe-dragging from the central black hole. This geometry adds a logarithmic termto the gravitational potential: Φ(r) = −GMb/r − v2flat ln(r/Rg). From this singlemodification, Vortex Dynamics derives: 1) flat rotation curves, 2) the BaryonicTully-Fisher Relation v4flat ∝ Mb, and 3) the MOND acceleration scale a0 = G/V ∗2with V ∗ = 0.338 kpc M−1/2⊙ as a universal constant. Comparison with Milky Wayand SPARC galaxy rotation curves shows Vortex reduces χ2 by 5× vs Newton andmatches data to < 3% using only baryonic mass. No free parameters per galaxyare required. Dark matter becomes unnecessary at galactic scales.

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