Abstract

 

The dynamics of galaxies present a long-standing challenge to gravitational theory. While Newtonian gravity and General Relativity describe solar-system phenomena with high precision, observed galactic rotation curves deviate systematically from the inverse-square expectation at large radii.

In this work, we explore an alternative approach in which gravitational influence is treated as a conserved outward transport that undergoes progressive redistribution through interaction with the vacuum. Modeling this redistribution as a stochastic scattering process using a Poisson description, leads to a closed-form analytical expression for the gravitational field,​

 

which describes a continuous transition from a geometry-dominated inverse-square regime to a redistribution-dominated  regime. When combined with the mass-dependent transport scale , this framework yields an asymptotic field , consistent with the empirical baryonic Tully–Fisher relation. Furthermore, the emergence of an effective  regime influences the dynamics of galactic cores, where distance-enhanced gravitational contributions lead to a breakdown of Newton’s shell theorem and naturally produce stiff-core rotation.

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Within this framework, galactic dynamics arise from transport behavior and statistical self-interaction, allowing a consistent description based solely on baryonic matter, without introducing additional matter components. The resulting force law applies across different galactic scales without parameter tuning, providing a predictive and testable description of observed galactic kinematics.