Galaxy Rotation Curves and Baryonic Scaling Relations in Time-Field General Relativity: A Systematic Analysis of the SPARC Sample

We present a systematic phenomenological analysis of galaxy rotation curves in the framework of Time-Field General Relativity (TFGR), using the SPARC database of late-type galaxies [Lelli et al., 2016]. The working hypothesis is that galactic dynamics may encode a finite response scale in gravitational behavior, represented here by a TFGR-inspired velocity profile with saturation velocity V0, transition radius rc, and transition sharpness n. We compare this profile with baryonic-only rotation curves built from the observed gas, stellar disk, and bulge contributions. Across 165 successful fits, the TFGR profile improves upon the baryonic-only description in 157 galaxies, with a median improvement of ΔAIC ≃ 331. The median reduced chi-square decreases from χ2ν ≃ 18.5 for baryonic-only models to χ2ν ≃ 0.41 for TFGR fits. In a robust subsample of 34 galaxies, the TFGR saturation velocity closely tracks the observed outer rotation velocity, with a tight correlation between V0 and Vflat. We further examine baryonic Tully–Fisher-like relations and structural scaling relations involving rc. The transition radius exhibits a weak positive trend with global galaxy size and disk scale length, while the ratio rc/Rdisk has a median value of about 1.8. These results indicate that the TFGR phenomenological profile captures systematic regularities in the SPARC sample and motivates further investigation of whether galaxy rotation curves may encode a characteristic dynamical response scale.