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

Why It Matters

If TFGR reliably captures rotation‑curve behavior, it offers a testable alternative to dark‑matter explanations and could reshape scaling‑relation models across galaxy populations.

Key Takeaways

• TFGR fits improve rotation curves in 157 of 165 galaxies.
• Median ΔAIC rises ~331, chi‑square drops to 0.41.
• Saturation velocity V0 tightly matches observed Vflat.
• Transition radius rc averages 1.8 × disk scale length.
• Weak positive trend between rc and overall galaxy size.

Pulse Analysis

Galaxy rotation curves have long exposed the missing‑mass problem, underpinning the dark‑matter paradigm. Yet alternative gravity theories aim to reproduce observed kinematics without unseen particles. Time‑Field General Relativity (TFGR) proposes a finite response scale, expressed as a saturated velocity profile with three parameters: maximum speed (V0), transition radius (rc), and sharpness exponent (n). By fitting these directly to rotation data, TFGR seeks systematic trends that baryonic‑only models overlook. Such a framework also links rotation‑curve morphology to baryonic scaling laws, potentially unifying disparate empirical relations under a single gravitational description.

Applying the TFGR profile to 165 SPARC late‑type galaxies, researchers compared it with baryonic‑only rotation curves. TFGR achieved superior fits in 157 cases, improving the median Akaike Information Criterion by ~331 points and dropping the reduced chi‑square from 18.5 to 0.41. In a subset of 34 galaxies, the saturation velocity V0 matches the observed flat rotation speed, indicating a universal outer‑disk limit. The transition radius rc averages 1.8 × the disk scale length and shows a modest positive correlation with overall galaxy size. The weak rc‑size correlation suggests that the response scale expands modestly with galaxy growth, offering a quantitative handle on structural evolution.

If TFGR consistently reproduces rotation curves, it challenges the exclusivity of dark‑matter explanations and offers a new testbed for modified gravity. Upcoming studies must examine dwarf and high‑redshift galaxies, and integrate TFGR into cosmological simulations to verify compatibility with large‑scale structure observations. Precision measurements from upcoming facilities like the Vera C. Rubin Observatory will be crucial for discriminating TFGR signatures from dark‑matter halo predictions. A validated dynamical response scale could reshape interpretations of the Tully‑Fisher relation and other mass‑distribution diagnostics, influencing future survey strategies in precision astronomy.