
TL;DR
This paper investigates spacetimes characterized by connections that are locally but not globally Levi-Civita, offering a new perspective beyond the traditional global metric approach, with an example based on Robertson-Walker spacetimes.
Contribution
It introduces a method to construct spacetimes using connections that are locally Levi-Civita but not globally, expanding the framework of spacetime geometry.
Findings
Provides a general method for non-degenerate connections
Presents an example modifying Robertson-Walker spacetimes
Explores implications of locally metric connections
Abstract
Spacetimes have conventionally been described by a global Lorentzian metric on a differentiable four-manifold. Herein we explore the possibility of spacetimes defined by a connection, which is locally but not globally Levi-Civita. The general method of obtaining such connections is presented for the non-degenerate case followed by an example that modifies the Robertson-Walker spacetimes for flat spacelike hypersurfaces.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Mathematics and Applications
