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Flächenbelegungen und Topologie in der allgemeinen Relativitätstheorie
Author(s) -
Treder HansJürgen
Publication year - 1970
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19704790507
Subject(s) - geodesic , physics , surface (topology) , manifold (fluid mechanics) , metric (unit) , completeness (order theory) , mathematics , pure mathematics , mathematical analysis , geometry , mechanical engineering , operations management , engineering , economics
The definition of a surface density of matter on a surface ∑ by essential discontinuities of the first derivations of the metric g μν across ∑ is depending on the geodesic completeness of the manifold and on the hypothesis g ± 0. We give a general definition of surface densities and we prove that some cases of geodesic incompleteness of the manifold are corresponding to surface densities of matter.