Distributional geometry in general relativity

DOI10.1016/j.geomphys.2011.04.018zbMath1242.53098OpenAlexW2015431237WikidataQ126002211 ScholiaQ126002211MaRDI QIDQ764525

D. Kharzeev

Publication date: 13 March 2012

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2011.04.018

zbMATH Keywords

general relativitycosmic stringsColombeau algebrasdistributional geometry

Mathematics Subject Classification ID

String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Applications of global differential geometry to the sciences (53C80) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Distributions, generalized functions, distribution spaces (46F99)

Related Items (6)

Nonlinear generalized sections of vector bundles ⋮ Some results on Kenmotsu statistical manifolds ⋮ Unifying order structures for Colombeau algebras ⋮ The Yamabe problem for distributional curvature ⋮ Spacetimes with distributional semi-Riemannian metrics and their curvature ⋮ Calculus of variations and optimal control for generalized functions

Cites Work

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• A global theory of algebras of generalized functions. II. Tensor distributions
• Generalized functions and multiplication of distributions on \({\mathcal C}^ \infty\) manifolds
• A global theory of algebras of generalized functions
• Definition and stability of Lorentzian manifolds with distributional curvature
• Generalized Hamiltonian mechanics. A mathematical exposition of non-smooth dynamical systems and classical Hamiltonian mechanics
• On the foundations of nonlinear generalized functions I and II
• Generalized pseudo-Riemannian geometry
• On the Geroch–Traschen class of metrics
• Borel's theorem for generalized functions
• Distributional curvature of time dependent cosmic strings
• Distributional energy - momentum tensor of the extended Kerr geometry
• Distributional geometry
• The ultrarelativistic Reissner–Nordstro/m field in the Colombeau algebra
• Intrinsic Characterization of Manifold-Valued Generalized Functions
• Invariance of the distributional curvature of the cone under smooth diffeomorphisms
• `Elementary flatness' on a symmetry axis
• Generalized functions and distributional curvature of cosmic strings
• Metrics with distributional curvature
• The use of generalized functions and distributions in general relativity
• Sur la méthode de généralisation de M. Laurent Schwartz et sur la convergence faible
• Multiplication of distributions
• Junction conditions for null hypersurfaces

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