Spacetimes with distributional semi-Riemannian metrics and their curvature

JOURNAL OF GEOMETRY AND PHYSICS

卷:151

Article

Nigsch, E. A.¹ 

[1] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

关键词: Nonlinear generalized functions;    Singular metric;    Conical metric;    Colombeau algebra;    Distributional section;   

DOI  :  10.1016/j.geomphys.2020.103623

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free