Spaces with torsion from embedding and the special role of autoparallel trajectories

Details Spaces with torsion from embedding and the special role of autoparallel trajectories Spaces with torsion from embedding and the special role of autoparallel trajectories

1997-09-25

arxiv.org/abs/gr-qc/9709067v1

Phys.Lett. B428 (1998) 315-321

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX file in src, no figures. Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also

Scientific paper

10.1016/S0370-2693(98)00421-3

As a contribution to the ongoing discussion of trajectories of spinless particles in spaces with torsion we show that the geometry of such spaces can be induced by embedding their curves in a euclidean space without torsion. Technically speaking, we define the tangent (velocity) space of the embedded space imposing non-holonomic constraints upon the tangent space of the embedding space. Parallel transport in the embedded space is determined as an induced parallel transport on the surface of constraints. Gauss' principle of least constraint is used to show that autoparallels realize a constrained motion that has a minimal deviation from the free, unconstrained motion, this being a mathematical expression of the principle of inertia.

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