Sheaves of Einstein algebras |
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Authors: | Michael Heller Wiesław Sasin |
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Affiliation: | (1) Cracow Group of Cosmology, Cracow, Poland;(2) Vatican Observatory, V-00120 Vatican City State;(3) Technical University of Warsaw, Plac Politechniki 1, 00-661 Warsaw, Poland |
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Abstract: | To include all types of singularities into a geometrically tractable theoretical scheme we change from Einstein algebras, an algebraic generalization of general relativity, to sheaves of Einstein algebras. The theory of such spaces, called Einstein structured spaces, is developed. Both quasiregular and curvature singularities are studied in some detail. Examples of the closed Friedmann world model and the Schwarzschild spacetime show that Schmidt'sb-boundary is a useful theoretical tool when considered in the category of structured spaces. |
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