On the geometric meaning of general relativity and the foundations of Newtonian cosmology

The geometric foundations of General Relativity are revisited here, 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 i...

Descripción completa

Detalles Bibliográficos
Autores: Haro Cases, Jaume|||0000-0002-5705-2405, Elizalde Rius, Emilio
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/452157
Acceso en línea:https://hdl.handle.net/2117/452157
https://dx.doi.org/10.3390/appliedmath5040142
Access Level:acceso abierto
Palabra clave:Newtonian mechanics
Friedmann equations
Differential geometry
Àrees temàtiques de la UPC::Física::Astronomia i astrofísica::Cosmologia i cosmogonia
Descripción
Sumario:The geometric foundations of General Relativity are revisited here, 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.