Covariance, Geometricity, Setting, and Dynamical Structures on Cosmological Manifold

Vladimir S. Mashkevich

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Covariance, Geometricity, Setting, and Dynamical Structures on Cosmological Manifold

Vladimir S. Mashkevich

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Abstract

The treatment of the principle of general covariance based on coordinate systems, i.e., on classical tensor analysis suffers from an ambiguity. A more preferable formulation of the principle is based on modern differential geometry: the formulation is coordinate-free. Then the principle may be called ``principle of geometricity.'' In relation to coordinate transformations, there had been confusions around such concepts as symmetry, covariance, invariance, and gauge transformations. Clarity has been achieved on the basis of a group-theoretical approach and the distinction between absolute and dynamical objects. In this paper, we start from arguments based on structures on cosmological manifold rather than from group-theoretical ones, and introduce the notion of setting elements. The latter create a scene on which dynamics is performed. The characteristics of the scene and dynamical structures on it are considered.

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BibTeX RIS

Vladimir S. Mashkevich. 2006-03-14. Covariance, Geometricity, Setting, and Dynamical Structures on Cosmological Manifold. https://arxiv.org/abs/gr-qc/0603053

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