Calculating Galactic Rotation Curves Using Spatial-Causal Geometry: A New Approach to Gravitational Dynamics

This study presents Spatial-Causal Geometry (SCG) as an alternative framework to dark matter in explaining galactic rotation curves. Instead of treating gravity as a fundamental force requiring unseen mass, SCG models it as an emergent effect of spatial-density gradients, directly linking rotation velocities to the geometric structure of space.

Using observational data from the SPARC database, this research applies a power-law spatial-density profile to fit galactic rotation curves without the need for dark matter halos. A best-fit analysis yields an optimal density gradient exponent , closely aligning with theoretical SCG predictions and demonstrating strong empirical agreement across multiple galaxy types.

Key Findings:

SCG Accurately Predicts Rotation Curves: Empirical validation shows that SCG-derived rotation velocities match observed data without requiring dark matter assumptions.

Best-Fit Analysis Confirms Theoretical Predictions: The derived exponent  aligns closely with theoretical expectations.

Cosmological Implications: SCG predicts measurable gravitational lensing deviations, alternative large-scale structure formation mechanisms, and refinements to existing cosmological models.

By reframing gravity as a geometric phenomenon, SCG challenges conventional astrophysical paradigms, offering a testable, falsifiable alternative to dark matter-based models.

Keywords:

Galactic rotation curves, Spatial-Causal Geometry (SCG), Dark matter alternatives, Gravitational dynamics, Power-law density gradients, SPARC database, Best-fit modeling, Gravitational lensing predictions, Large-scale structure formation, Cosmological implications