Frames of reference in spaces with affine connections and metrics

Details Frames of reference in spaces with affine connections and metrics Frames of reference in spaces with affine connections and metrics

1999-08-24

arxiv.org/abs/gr-qc/9908061v1

Class.Quant.Grav.18:1111-1126,2001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, LaTeX 2e

Scientific paper

10.1088/0264-9381/18/6/310

A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects: (a) a non-null (non-isotropic) vector field, (b) the orthogonal to the vector field sub space, (c) an affine connection and the related to it covariant differential operator determining a transport along the given non-null vector filed. On the grounds of this definition other definitions related to the notions of accelerated, inertial, proper accelerated and proper inertial frames of reference are introduced and applied to some mathematical models for the space-time. The auto-parallel equation is obtained as an Euler-Lagrange's equation. Einstein's theory of gravitation appears as a theory for determination of a special frame of reference (with the gravitational force as inertial force) by means of the metrics and the characteristics of a material distribution. PACS numbers: 0490, 0450, 1210G, 0240V

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