Normal frames and the validity of the equivalence principle. I. Cases in a neighborhood and at a point

Abstract

A treatment in a neighborhood and at a point of the equivalence principle on the basis of derivations of the tensor algebra over a manifold is given. Necessary and sufficient conditions are given for the existence of local bases, called normal frames, in which the components of derivations vanish in a neighborhood or at a point. These frames (bases), if any, are explicitly described and the problem of their holonomicity is considered. In particular, the obtained results concern symmetric as well as nonsymmetric linear connections.

arXiv commentLaTeX2e, 9 pages, to be published in Journal of Physics A: Mathematical and General

References in corpus (1)

• Normal frames for non-Riemannian connections

Cited by in corpus (13)

• Gravitational ultrarelativistic spin-orbit interaction and the weak equivalence principle
• Normal frames and the validity of the equivalence principle
• Is the principle of equivalence a principle?
• Normal frames and the validity of the equivalence principle. III. The case along smooth maps with separable points of self-intersection
• Dirac-type equations in a gravitational field, with vector wave function
• General reference frames and their associated space manifolds
• Gravitation as Anholonomy
• Auto-parallel equation as Euler-Lagrange's equation in spaces with affine connections and metrics
• Frames of reference in spaces with affine connections and metrics
• Locally Inertial Reference Frames in Lorentzian and Riemann-Cartan Spacetimes
• Deviation equations of Synge and Schild over spaces with affine connections and metrics
• Flows and particles with shear-free and expansion-free velocities in (L^-_n,g)- and Weyl's spaces
• On the existence of a gyroscope in spaces with affine connections and metrics