Fibre bundles, connections, general relativity, and Einstein-Cartan theory
Miguel Socolovsky
TL;DR
This paper explores the geometric foundations of General Relativity and Einstein-Cartan theory using the language of fiber bundles and connections, providing a natural mathematical framework for these theories.
Contribution
It introduces a geometric formulation of GR and Einstein-Cartan theory through vector and principal bundles, clarifying their mathematical structure.
Findings
Unified geometric description of GR and Einstein-Cartan theory
Clarification of connection roles in these theories
Mathematical framework enhances understanding of spacetime geometry
Abstract
We present in the most natural way, that is, in the context of the theory of vector and principal bundles and connections in them, fundamental geometrical concepts related to General Relativity and one of its extensions, the Einstein-Cartan theory.
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Taxonomy
TopicsCosmology and Gravitation Theories · Advanced Differential Geometry Research · Black Holes and Theoretical Physics