Normal frames and the validity of the equivalence principle. III. The case along smooth maps with separable points of self-intersection

Details Normal frames and the validity of the equivalence principle. III. The case along smooth maps with separable points of self-intersection Normal frames and the validity of the equivalence principle. III. The case along smooth maps with separable points of self-intersection

1998-05-22

arxiv.org/abs/gr-qc/9805088v1

J.Phys.A31:1287-1296,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 standard LaTeX 2e (11pt, A4) pages. The package amsfonts is required

Scientific paper

10.1088/0305-4470/31/4/016

The equivalence principle is treated on a mathematically rigorous base on sufficiently general subsets of a differentiable manifold. This is carried out using the basis of derivations of the tensor algebra over that manifold. Necessary and/or sufficient conditions of existence, uniqueness, and holonomicity of these bases in which the components of the derivations of the tensor algebra over it vanish on these subsets, are studied. The linear connections are considered in this context. It is shown that the equivalence principle is identically valid at any point, and along any path, in every gravitational theory based on linear connections. On higher dimensional submanifolds it may be valid only in certain exceptional cases.

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