Abstract

This paper proposes an extension to General Relativity by incorporating kinetic energy (velocity/momentum) directly into the spacetime metric alongside mass, completing the equivalence principle. This is done by introducing a modified Schwarzschild metric where a velocity factor ±(v²/c²) is added to the traditional gravitational factor 2GM/rc², one consequence being that spatial deformations occur in 3D for macro-scale gravitational/kinetic systems. The new metric offers potential frameworks for explaining galactic rotation curves (e.g., Andromeda) without relying heavily on Dark Matter, as well as accounting for cosmic expansion without requiring Dark Energy. The paper presents potential experimental tests to distinguish between traditional special relativity time dilation and this new general relativity kinetic dilation, including single-direction light-speed measurements using long-baseline interferometers (such as LIGO) with high-precision atomic clocks.

It seems there is an equivalence between Special Relativity time dilation/length contraction factors and General Relativity potential terms. But to talk about unification would be premature.

The paper also argues against a universal speed of light and instead posits that the speed of light is relative to local physical "systems" (defined by local dominant masses like Earth, the Sun, or galaxies). Special relativity is treated as a local phenomenon within these systems and presents a Variable Speed of Light theory.

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