Selected geometrical and physicsl aspects of conformal transformations

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Selected geometrical and physicsl aspects of conformal transformations

Journal Title: Problemy Nauk Stosowanych - Year 2015, Vol 3, Issue

Abstract

Introduction and aims: The conformal transformations play the crucial role in the analysis of the global structure of the space-time. The main goal of this article is to present the consequences of the conformal transformation of the metric like the creation of the energy and momentum for the gravitational field or the creation of the matter. Material and methods: In the paper have been proved the transformation formulas for some geometrical and physical objects. The analytical methods have been used in the paper. Results: In the paper there were proved the transformation formulas of the affine connection, the covariant derivative, the geodesics, the curvature tensor, the Ricci tensor, the curvature scalar and the Weyl tensor. The Einstein’s equations were proved not to be invariant under the conformal rescaling of the metric, as well as the Landau-Lifshitz pseudotensor. Conclusion: The article shows that the conformal rescaling of the metric creates a new matter and an additional energy and momentum of the gravity. There is also possibility of creation of the Friedman universes from the vacuum.

Authors and Affiliations

Marta Dudek

Keywords

Conformal transformation of the metric general theory of relativity space-time Riemannian manifold pseudo-Riemannian manifold Lorentzian manifold Einstein’s equations Landau-Lifshitz pseudotensor of the energy-momentum.

EP ID EP165126
DOI -
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