On the completeness of impulsive gravitational wave spacetimes

2012/07/31 by Clemens Sämann, Roland Steinbauer
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Mathematical Physics Problems #Class (philosophy) #Completeness (order theory) #Dimension (graph theory) #Dirac (video compression format) #Geometric Analysis and Curvature Flows #Gravitation #Gravitational wave #Manifold (fluid mechanics) #Riemannian manifold #gr-qc #math-ph #math.MP #msc:46F10 #msc:83C15 #msc:83C35

paper · pdf · doi:10.1088/0264-9381/29/24/245011

published as Class. Quantum Grav. 29 (2012) 245011 (11pp) · 13 pages, minor changes suggested by the referees

arxiv created 2012/11/19 · openalex publication_date 2012/11/23 · arxiv updated 2012/11/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We consider a class of impulsive gravitational wave space-times, which generalize impulsive pp-waves. They are of the form M=N×ℝ²₁, where (N,h) is a Riemannian manifold of arbitrary dimension and M carries the line element ds²=dh²+ 2dudv+f(x)δ(u)du² with dh² the line element of N and δ the Dirac measure. We prove a completeness result for such space-times M with complete Riemannian part N.

Citations

• The use of Generalised Functions and Distributions in General Relativity
• Einstein spaces which are mapped conformally on each other
• Manifolds, Tensor Analysis, and Applications