General Relativity as a Genuine Connection Theory

Details General Relativity as a Genuine Connection Theory General Relativity as a Genuine Connection Theory

2004-12-07

arxiv.org/abs/gr-qc/0412032v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 14 pages. Talk presented at the colloquium "Theory and Experiment in Cosmology and Gravitation", in honor of Jose Plini

Scientific paper

The Palatini formulation is used to develop a genuine connection theory for general relativity, in which the gravitational field is represented by a Lorentz-valued spin connection. The existence of a tetrad field, given by the Fock-Ivanenko covariant derivative of the tangent-space coordinates, implies a coupling between the spin connection and the coordinate vector-field, which turns out to be the responsible for the onset of curvature. This connection-coordinate coupling can thus be considered as the very foundation of the gravitational interaction. The peculiar form of the tetrad field is shown to reduce both Bianchi identities of general relativity to a single one, which brings this theory closer to the gauge theories describing the other fundamental interactions of Nature. Some further properties of this approach are also examined.

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