On the Dynamics of Celestial Bodies: Dark Matter

Abstract

We develop a mathematical mechanism for dark-matter phenomenology by retaining the causal and nonlinear Einstein dynamics before applying finite-resolution approximations. Finite conserved world tubes generate a retarded metric, whose unresolved historical component defines a conserved effective geometric source without introducing additional matter. Correlated microscopic histories accumulate, while quadratic Einstein interactions rectify fluctuating modes into static or slowly varying collective curvature. A general causal decay law prevents indefinite accumulation and establishes a finite balance between continual replenishment and dissipation. In the weak-field regime, the resulting historical metric governs orbital dynamics, tidal effects, and gravitational lensing through the same geometry. Its radial scaling accommodates cores, transition regions, approximately flat rotation curves, and finite-range outer decay without prescribing a dark-matter halo profile. The resulting curvature is extended, structure-attached, causal, temporally persistent, and lensing-active, reproducing the principal qualitative properties commonly attributed to dark matter. This construction provides a general-relativistic mechanism for dark-matter phenomenology, while the microscopic origin of the effective decay law remains open. **Keywords** celestial-body dynamics; general relativity; dark matter; historical spacetime dynamics; retarded gravitational fields; geometric memory; nonlinear mode coupling; spacetime coarse graining; galactic dynamics; gravitational lensing