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General relativity extended to nonRiemannian spacetime geometry. eprint 0910.3582v7
"... Abstract: The gravitation equations of the general relativity, written for Riemannian spacetime geometry, are extended to the case of arbitrary (nonRiemannian) spacetime geometry. The obtained equations are written in terms of the world function in the coordinateless form. These equations determi ..."
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Abstract: The gravitation equations of the general relativity, written for Riemannian spacetime geometry, are extended to the case of arbitrary (nonRiemannian) spacetime geometry. The obtained equations are written in terms of the world function in the coordinateless form. These equations determine directly the world function, (but not only the metric tensor). As a result the spacetime geometry appears to be nonRieamannian. Invariant form of the obtained equations admits one to exclude in
uence of the coordinate system on solutions of dynamic equations. Anybody, who trusts in the general relativity, is to accept the extended general relativity, because the extended theory does not use any new hypotheses. It corrects only inconsequences and restrictions of the conventional conception of general relativity. The extended general relativity predicts an induced antigravitation, which eliminates existence of black holes.
Different representations of Euclidean geometry
, 2008
"... Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In Erepresentation there are three basic elements (point, segment, angle) and no additional structures. Vrepresentation c ..."
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Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In Erepresentation there are three basic elements (point, segment, angle) and no additional structures. Vrepresentation contains two basic elements (point, vector) and additional structure: linear vector space. In σrepresentation there is only one basic element and additional structure: world function σ = ρ 2 /2, where ρ is the distance. The concept of distance appears in all representations. However, as a structure, determining the geometry, the distance appears only in the σrepresentation. The σrepresentation is most appropriate for modification of the proper Euclidean geometry. Practically any modification of the proper Euclidean geometry turns it into multivariant geometry, where there are many vectors Q0Q1,Q0Q ′ 1,..., which are equal to the vector P0P1, but they are not equal between themselves, in general.