Published April 10, 2026 | Version v3
Preprint Open

Self-Interacting Gravity and the Transition from Radial to Transport-Dominated Gravitational Dynamics

Authors/Creators

Description

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.

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.

 

Notes

The discrepancy between Newtonian gravity and galactic rotation curves is traditionally solved by introducing invisible dark matter. This paper presents a fundamental analytical alternative: gravitation operates as a conserved, continuous outward transport of influence that undergoes progressive redistribution through elastic interactions with the vacuum medium.

This framework derives large-scale galactic kinematics natively from transport conservation and statistical mechanics, built across five analytical pillars:

·        1. A Unified Force Law: By treating gravity as a conserved flux, the progressive sharing of influence reduces effective drift velocity and builds transport density. This yields a single force law that smoothly bridges the classical inverse-square (1/r^2) baseline and the redistributed (1/r) geometry.

·        2. Dual Interaction Regimes: Transport encountering structured baryonic matter interacts with the full classical source mass (M). Conversely, when propagating through empty space, the vacuum couples only to the statistical fluctuation of the field, scaling natively as sqrt (M).

·        3. Native Tully-Fisher Derivation: Equating the classical field density to a universal vacuum threshold (a_0) establishes a dynamic, mass-dependent macroscopic transition scale (λ). This formally derives the Baryonic Tully-Fisher relation (V^4=GMa_0) as an inevitable geometric consequence of scattered transport.

·        4. Core Dynamics and Shell Theorem Breakdown: Inside a partly redistributed  transport regime, exact spatial cancellation fails. Distant mass elements undergo more redistribution than nearby ones, naturally generating the harmonic restoring forces required to explain stiff-core, solid-body rotation.

·        5. Strict Falsifiability: Unlike phenomenological models that allow arbitrary tuning of dark matter halos, this framework culminates in a rigidly constrained master equation (Eq. 2.23). Governed solely by baryonic mass and a single universal vacuum constant, the model is strictly predictive and highly falsifiable against galactic kinematic data.

Files

260410 Self-Interacting Gravity and Transport Dynamics.pdf

Files (614.4 kB)

Additional details

Additional titles

Alternative title
Deriving Flat Rotation Curves and Harmonic Galactic Cores without Dark Matter or MOND
Alternative title
Deriving the Baryonic Tully-Fisher Relation and Harmonic Galactic Cores from Vacuum Transport