The cornerstone role of the torsion in Finslerian physical worlds

Details The cornerstone role of the torsion in Finslerian physical worlds The cornerstone role of the torsion in Finslerian physical worlds

Jun 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995gregr..27..629v&link_type=abstract

General Relativity and Gravitation, Volume 27, Issue 6, pp.629-644

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It is shown that there are no metric-compatible connections with zero torsion onproperly Finslerian, i.e. post-Riemannian, metrics. Since Finslerian connections exist on Riemannian metrics, the torsion rather than the metric becomes the object which determines whether the geometry is properly Finslerian or not. On the other hand, the solder forms and connection are determined by the torsion if the affine curvature is zero, the torsion then containing all the information about the geometric reality of spacetime. Since the metric curvature may still be Riemannian, the question arises of whether its present central role in spacetime physics is but a consequence of requiring that all the geometric content of spacetime be contained in the metric.

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