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Collapsing 4D Pseudo-Riemannian Metric Tensors into an Irreducible, Scale-Invariant Algebraic Scalar Equation. Reducing Computational Complexity to a Maximum of O(N) Universal (N-Body) and O(1) Instantaneous (2>3-Body)

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Zenodo
DOI
10.5281/zenodo.21349515

We present an exact algebraic reduction of General Relativity, demonstrating how complex four-dimensional pseudo-Riemannian metric tensors and multi-variable calculus can be collapsed into a single, static, closed-form scalar force equation. This equation integrates three distinct, interdependent mathematical components into a single static formula to yield an instantaneous, deterministic force value that unifies gravitational mechanics with the vacuum electromagnetic field ε0 in a single algebraic relation. Building upon the foundations established by Newton, Gauss, Maxwell, Einstein, and Lorentz, we demonstrate how this mathematical framework models orbital parameters consistent with Jet Propulsion Laboratory (JPL) data, illustrating that time is not an intrinsic component of space. While motion cannot exist without time, this framework shows that gravitational orbital movements are precisely calculated without time. Furthermore, this paper provides a universal mathematical definition for velocity, derives the equation necessary to precisely calculate a universal time while accounting for time dilation, and preserves the established framework for general relativistic observations such as gravitational lensing, frame dragging, and redshift. We separate time dilation into kinematic and gravitational time dilation independently, showing a universe ruled by the mathematical geometry of space and gravity.

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