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- W1508969735 abstract "We show that the necessary and sucient condition for erecting locally inertial coordinates at a point p of a U 4 -space, and the- refore 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 an- tisymmetric one. As an application, we derive the geodesic deviation equation; and prove the compatibility with the Newtonian limit. The problem of the validity of the equivalence principle (EP) in gra- vity theories with torsion and zero non-metricity (1), (2), has been discus- sed by several authors (3), (4), (5). The strategy of these authors consisted in showing the existence of local basis or normal frames such that, with respect to them, all components of the linear connection, which gives the gravitational force, vanish at a given point of the manifold (von der Heyde, Hartley) or also in a neighborhood of the point (Iliev). The pur- pose of the present article is to show that a particularly simple change of coordinates, can also maintain the validity of the EP in the presence of torsion, with the only restriction of this being totally antisymmetric. This is allowed by the structure of the geodesic equation. Using the fact that only the symmetric part of the connection intervenes in this equation, in section 2 we show that a necessary and sucient condition for the vanishing of the first derivatives of the metric is the vanishing" @default.
- W1508969735 created "2016-06-24" @default.
- W1508969735 creator A5090740957 @default.
- W1508969735 date "2010-09-21" @default.
- W1508969735 modified "2023-10-01" @default.
- W1508969735 title "Locally inertial coordinates with totally antisymmetric torsion" @default.
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