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arXiv · 0912.2858

Variational principle and free falling in a space-time with torsion

Rolando Gaitan D.·Juan Petit·Alfredo Mejía
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Abstract

A comparison between the two possible variational principles for the study of a free falling spinless particle in a space-time with torsion is noted. It is well known that the autoparallel trajectories can be obtained from a variational principle based on a non-holonomic mapping, starting with the standard world-line action. In a contrast, we explore a world-line action with a modified metric, thinking about the old idea of contorsion (torsion) potentials. A fixed-ends variational principle can reproduce autoparallel trajectories without restrictions on space-time torsion. As an illustration we have considered a perturbative Weitzenb$\ddot{o}$ck space-time. The non-perturbative problem is stablished at the end.

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Rolando Gaitan D., Juan Petit, Alfredo Mejía. 2009-12-15. Variational principle and free falling in a space-time with torsion. https://arxiv.org/abs/0912.2858

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