Anti-Gravity from Vacancies in Fractal Space-Time: The Case of a Menger Sponge
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908651499814912 |
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| author | Svozil, Karl |
| author_facet | Svozil, Karl |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15789 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anti-Gravity from Vacancies in Fractal Space-Time: The Case of a Menger Sponge Svozil, Karl General Relativity and Quantum Cosmology 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. |
| title | Anti-Gravity from Vacancies in Fractal Space-Time: The Case of a Menger Sponge |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2401.15789 |