Frames of reference in spaces with affine connections and metrics

Abstract

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

17 pages, LaTeX 2e

References in corpus (4)

• Riemann normal coordinates, Fermi reference system and the geodesic deviation equation
• Auto-parallel equation as Euler-Lagrange's equation in spaces with affine connections and metrics
• Conformal derivative and conformal transports over spaces with contravariant and covariant affine connections and metrics
• Conformal derivative and conformal transports over spaces with an affine connection and metrics

Cited by in corpus (5)

• Metric-affine Geometries With Spherical Symmetry
• Volume elements and torsion
• Cubic Algebraic Equations in Gravity Theory, Parametrization with the Weierstrass Function and Non-Arithmetic Theory of Algebraic Equations
• The Minkowski metric in non-inertial observer radar coordinates
• Flows and particles with shear-free and expansion-free velocities in (L^-_n,g)- and Weyl's spaces