Generalized pseudo-Riemannian geometry

DOI10.1090/S0002-9947-02-03058-1zbMath1012.46049arXivmath/0107057MaRDI QIDQ3151226

Michael Kunzinger, Roland Steinbauer

Publication date: 7 October 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0107057

zbMATH Keywords

general relativityColombeau algebrasalgebras of generalized functionsgeneralized tensor fieldsgeneralized metric(generalized) pseudo-Riemannian geometry

Mathematics Subject Classification ID

Operations with distributions and generalized functions (46F10) Distributions and generalized functions on nonlinear spaces (46T30) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Related Items (26)

Nonlinear generalized sections of vector bundles ⋮ Nonsmooth differential geometry and algebras of generalized functions ⋮ Sheaves of nonlinear generalized functions and manifold-valued distributions ⋮ Optimal embeddings of ultradistributions into differential algebras ⋮ On regularization of vector distributions on manifolds ⋮ Remarks on the distributional Schwarzschild geometry ⋮ Optimal regularization processes on complete Riemannian manifolds ⋮ The classical theory of calculus of variations for generalized functions ⋮ Nonlinear tensor distributions on Riemannian manifolds ⋮ Geodesics in nonexpanding impulsive gravitational waves with Λ. II ⋮ An algebraic approach to manifold-valued generalized functions ⋮ Hilbert $\widetilde{\mathbb{C}}$-modules: Structural properties and applications to variational problems ⋮ Foundations of the calculus of variations in generalized function algebras ⋮ Homogeneity in generalized function algebras ⋮ A nonlinear theory of distributional geometry ⋮ Distributional metrics and the action principle of Einstein–Hilbert gravity ⋮ The globally hyperbolic metric splitting for non-smooth wave-type space-times ⋮ Suppleness of the sheaf of algebras of generalized functions on manifolds ⋮ Inversion of Colombeau generalized functions ⋮ Generalized group actions in a global setting ⋮ Geometrical embeddings of distributions into algebras of generalized functions ⋮ The wave equation on singular space-times ⋮ Wave-type equations of low regularity ⋮ Distributional geometry in general relativity ⋮ A nonlinear theory of generalized functions ⋮ Algebras of generalized functions with smooth parameter dependence

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