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arXiv · 2401.15789

Anti-Gravity from Vacancies in Fractal Space-Time: The Case of a Menger Sponge

Karl Svozil
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Abstract

We explore the idea that anti-gravity, interpreted as matter-matter repulsion, may emerge as an effective description of spacetime with a reduced local ``substratum density,'' modeled heuristically by vacancies in a fractal lattice. Using the Menger Sponge as a prototypical vacancy-dominated fractal, we motivate a phenomenological identification of a net vacancy parameter with the mass parameter in the Schwarzschild solution. This yields an effective negative-mass Schwarzschild-like metric for embedded observers when vacancies dominate. We analyze curvature, geodesic motion, and energy-condition issues, and we emphasize that our construction is not a microscopic derivation from a specific stress-energy tensor but a re-interpretation of the negative-mass Schwarzschild geometry in terms of fractal vacancies. We discuss conceptual implications, stability challenges, and possible observational signatures.

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Karl Svozil. 2024-01-28. Anti-Gravity from Vacancies in Fractal Space-Time: The Case of a Menger Sponge. https://arxiv.org/abs/2401.15789

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