Journal
JOURNAL OF GEOMETRY AND PHYSICS
Volume 151, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.geomphys.2020.103623
Keywords
Nonlinear generalized functions; Singular metric; Conical metric; Colombeau algebra; Distributional section
Categories
Funding
- Austrian Science Fund (FWF) [P26859, P30233]
- Austrian Science Fund (FWF) [P26859] Funding Source: Austrian Science Fund (FWF)
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We develop a comprehensive geometric framework for defining spaces g(M, E) of non-linear generalized sections of vector bundles E -> M containing spaces of distributional sections D'(M, E). Our theory incorporates classical differential geometric operations (like tensor products, covariant derivatives and Lie derivatives), is localizable and fully compatible with smooth and distributional tensor calculus. As an application to the treatment of singular metrics, we calculate the curvature of the conical metric used to describe cosmic strings. (C) 2020 Elsevier B.V. All rights reserved.
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