Gravitation as Anholonomy

Details Gravitation as Anholonomy Gravitation as Anholonomy

2003-01-21

arxiv.org/abs/gr-qc/0301077v1

Gen.Rel.Grav. 35 (2003) 991-1005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

RevTeX4, 10 pages, no figures. To appear in Gen. Rel. Grav

Scientific paper

A gravitational field can be seen as the anholonomy of the tetrad fields. This is more explicit in the teleparallel approach, in which the gravitational field-strength is the torsion of the ensuing Weitzenboeck connection. In a tetrad frame, that torsion is just the anholonomy of that frame. The infinitely many tetrad fields taking the Lorentz metric into a given Riemannian metric differ by point-dependent Lorentz transformations. Inertial frames constitute a smaller infinity of them, differing by fixed-point Lorentz transformations. Holonomic tetrads take the Lorentz metric into itself, and correspond to Minkowski flat spacetime. An accelerated frame is necessarily anholonomic and sees the electromagnetic field strength with an additional term.

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