Abstract

 

The discrepancy between Newtonian dynamics in planetary systems and the flat rotation curves of galaxies is commonly attributed to non-baryonic dark matter. We propose an alternative dynamical framework in which gravity is modeled as directed transport of gravitational force through a self-interacting vacuum medium.

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In this picture, coherent radial gravity converses with distance due to elastic self-interaction among vacuum degrees of freedom. The mechanism is comparable to known fluid dynamics. The force is conserved but progressively shared among an increasing number of vacuum participants. This redistribution leads naturally to a radius-dependent transport coefficient , which in steady state produces a gravitational acceleration scaling as  (corresponding to a logarithmic potential), while effectively preserving the Newtonian  law within solar system.

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The model assumes that radial gravity self-interact with vacuum and scatters on average after a distance , yielding three distinct kinematic regimes without introducing dark matter or modifying the gravitational coupling: (i) strictly Newtonian planetary systems since  everywhere, protected by the equivalence principle; (ii) harmonic solid-body rotation in galactic cores arising from the non-applicability of the shell theorem under the  kernel; and (iii) flat rotation curves in galactic halos governed by the diffusive  regime. The model also scales well with dwarf galaxies and very large galaxies. The Baryonic Tully–Fisher relation  emerges as a geometric consequence of the transport transition of gravity. The stiff rotation curve of the galactic core emerges for the same reason, but with different resulting dynamics in a denser environment.

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This framework preserves the constancy of  and the local validity of General Relativity, while attributing galactic-scale anomalies to vacuum transport geometry rather than unseen mass.