https://doi.org/10.1140/epjc/s10052-025-15119-4
Regular Article - Theoretical Physics
Decomposition of the connection in affine models of gravity
Can the connection tell us something about the metric?
1
, Valparaiso, Chile
2
Departamento de Física, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaiso, Chile
3
Instituto de Física, Pontificia Universidad Católica de Valparaíso, Av. Brasil 2950, Valparaiso, Chile
4
, Montevideo, Uruguay
a
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Received:
8
September
2025
Accepted:
23
November
2025
Published online:
15
December
2025
Abstract
In physics geometrical connections are the mean to create models with local symmetries (gauge connections), as well as general diffeomorphisms invariance (affine connections). Here we study the irreducible tensor decomposition of connections on the tangent bundle of an affine manifold as used in the polynomial affine model of gravity (Castillo-Felisola et al. in Universe 11(3):102, 2025. https://doi.org/10.3390/universe11030102). This connection is the most general linear connection, which allows us to build metric independent, diffeomorphism invariant models. This set up includes parts of the connection that are associated with conformal and projective transformations.
© The Author(s) 2025
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