Published January 8, 2026
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A Geometric Solution to Flat Galaxy Rotation Curves Based on GR Gravitational Wave Memory Effects
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Abstract
(1) Theoretical Framework: This study, based on the spacetime memory effect and quadratic enhancementmechanism in General Relativity (GR), constructs the White River spacetime dynamics model. It aims to provide
a unified explanation for the dynamical behavior of galaxies across all mass scales within the GR framework,
without introducing dark matter. The flattening of galaxy rotation curves is not an anomaly but originates from the
intrinsic constraints of spacetime geometry (characterized by a logarithmic potential). It is a natural consequence of
General Relativity on galactic scales. The model simultaneously offers a theoretical interpretation for the observed
dark matter effects and provides several falsifiable predictions.
(2) Derivation and Validation: Through dual-path derivation from both the GR framework and phenomenolog
ical analysis, this study obtains a consistent equation for the dark matter effect. The core parameters are determined
through systematic analysis of a sample of 202 SPARC galaxies (including irregular dwarf galaxies, dwarf elliptical
galaxies, and giant elliptical galaxies, which are often avoided by other dark matter theories). Markov Chain Monte
Carlo Bayesian iteration (600,000 steps) was used for parameter fitting. The marginalized posterior distribution
shows a coefficient of determination R 2 = 0.9712 and a reduced chi-squared value of 16, indicating good constraint
accuracy. Subsequently, we performed a zero-parameter verification using 30 independent non-SPARC galaxy
samples (covering four galaxy types, spanning 3.4 orders of magnitude in mass). The verification achieved a
coefficient of determination of 0.9338 and a reduced chi-squared value of 7.22, demonstrating the universality of
the model. Throughout the fitting and verification process, the model used only the baryonic mass of the galaxies
as the sole parameter, without any targeted corrections for specific galaxies. This study is the first to achieve a
unified description of the complete dynamical sequence from dwarf irregular galaxies to giant elliptical galaxies
using a single equation derived from the first principles of General Relativity.
Theoretical derivation confirms that, under specific degeneracy conditions, the model can yield Modified
Newtonian Dynamics (MOND) and the Baryonic Tully-Fisher Relation (BTFR) from the first principles of GR.
This suggests that the White River theory has the potential to unify MOND (as an effective theory) and the BTFR
(as an empirical law) within the geometric-dynamic framework of General Relativity in the future.
(3) Implications and Outlook: The White River theory offers a new theoretical paradigm for galactic
dynamics, emphasizing the dominant role of spacetime geometric constraints. It provides a unified explanation
for the dynamics of galaxies of all masses and types without invoking dark matter, thereby possessing the core
conditions to become a foundational theory of galactic dynamics. This study has not yet constructed a dynamical
equation applicable to galaxy clusters, and the explanation of dark matter effects on cosmological scales requires
further expansion. Related content will be supplemented and refined in subsequent work.
(4) Code and data enabling full reproducibility of this work are available at https://doi.org/10.5281/zenodo.18079655
under a Creative Commons Attribution 4.0 International (CC BY 4.0) license.
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Additional details
Dates
- Updated
-
2026-01-08Added Appendix A
Software
- Repository URL
- https://doi.org/10.5281/zenodo.18079655
- Programming language
- Python
- Development Status
- Active
References
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