Normal frames and the validity of the equivalence principle

Abstract

We investigate the validity of the equivalence principle along paths in gravitational theories based on derivations of the tensor algebra over a differentiable manifold. We prove the existence of local bases, called normal, in which the components of the derivations vanish along arbitrary paths. All such bases are explicitly described. The holonomicity of the normal bases is considered. The results obtained are applied to the important case of linear connections and their relationship with the equivalence principle is described. In particular, any gravitational theory based on tensor derivations which obeys the equivalence principle along all paths, must be based on a linear connection.

14 pages, LaTeX 2e, the package amsfonts is needed

References in corpus (2)

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

Cited by in corpus (21)

• 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
• Normal frames for linear connections in vector bundles and the equivalence principle in classical gauge theories
• Conservation of energy-momentum of matter as the basis for the gauge theory of gravitation
• Normal frames and linear transports along paths in vector bundles
• Auto-parallel equation as Euler-Lagrange's equation in spaces with affine connections and metrics
• Gravitation as Anholonomy
• Locally Inertial Reference Frames in Lorentzian and Riemann-Cartan Spacetimes
• Frames of reference in spaces with affine connections and metrics
• 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
• Equivalence principle in classical electrodynamics
• Mechanics of Continuous Media in $({\bar{L}}_n,g)$-spaces. I. Introduction and mathematical tools
• Relative velocity and relative acceleration induced by the torsion in (pseudo) Riemannian spaces with torsion and in spaces with an affine connection and metrics
• On the existence of a gyroscope in spaces with affine connections and metrics
• Weyl's spaces with shear-free and expansion-free conformal Killing vectors and the motion of a free spinless test particle
• Normal frames for general connections on differentiable fibre bundles
• Doppler effect and Hubble effect in different models of space-time in the case of auto-parallel motion of the observer
• Determination of the velocity of an emitter in spaces with affine connections and metrics