Gorde:
| Egile nagusia: | |
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| Formatua: | Recurso digital |
| Hizkuntza: | |
| Argitaratua: |
Zenodo
2025
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| Sarrera elektronikoa: | https://doi.org/10.5281/zenodo.17687786 |
| Etiketak: |
Etiketa erantsi
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Aurkibidea:
- This paper explores the theoretical concept of metric phase transitions within the framework of geometries possessing constant curvature, namely Euclidean, spherical, and hyperbolic spaces. Drawing parallels from thermodynamic phase transitions, we propose that under certain conditions, a manifold's metric structure itself can undergo abrupt, non-analytic changes, leading to distinct geometric phases. The investigation delves into how external parameters, analogous to temperature or pressure, could induce such transformations, altering fundamental properties like topology, volume, or the very nature of spacetime intervals. We review established ideas in gravitational physics, condensed matter analogues, and pure geometry that hint at such phenomena. A theoretical methodology is outlined, involving the construction of effective geometric potentials or actions whose minima correspond to stable metric phases. The implications of these hypothetical transitions are discussed, extending to early universe cosmology, quantum gravity, and the stability of spacetime. This work aims to establish a foundational understanding for future investigations into the dynamic evolution and stability of geometric structures.