Locally inertial coordinates with totally antisymmetric torsion

Details Locally inertial coordinates with totally antisymmetric torsion Locally inertial coordinates with totally antisymmetric torsion

2010-09-21

arxiv.org/abs/1009.3979v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages

Scientific paper

We show that the necessary and sufficient condition for erecting locally inertial coordinates at a point $p$ of a $U^4$-space, and therefore assuring the validity of the equivalence principle at that point, is the vanishing at $p$ of the symmetric part of the contortion tensor. This fact does not demand a vanishing torsion, but only a totally antisymmetric one. As an application, we derive the geodesic deviation equation; and prove the compatibility with the Newtonian limit.

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