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arXiv · 2510.13934

On the Geometric Meaning of General Relativity and the Foundations of Newtonian Cosmology

Jaume de Haro·Emilio Elizalde
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Abstract

The geometric foundations of General Relativity are revisited, with particular attention to its gauge invariance, as a key to understanding the true nature of spacetime. Beyond the common image of spacetime as a deformable 'fabric' filling the Universe, curvature is interpreted as the dynamic interplay between matter and interacting fields; a view already emphasized by Einstein and Weyl, but sometimes overlooked in the literature. Building on these tools, a Newtonian framework is reconstructed that captures essential aspects of cosmology, showing how classical intuition can coexist with modern geometric insights. This perspective shifts the focus from substance to relationships, offering a fresh magnifying glass through which to reinterpret gravitational dynamics and the large-scale structure of the Universe. The similarities of this approach with other recent, more ambitious ones carried out at the quantum level are quite remarkable.

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Jaume de Haro, Emilio Elizalde. 2025-10-15. On the Geometric Meaning of General Relativity and the Foundations of Newtonian Cosmology. https://doi.org/10.3390/appliedmath5040142

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