2002/02/28 by Sergio M. C. V. Goncalves, Sérgio M. C. V. Gonçalves
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Energy condition #General relativity #Geodesic #Geodesics in general relativity #Gravitational collapse #Gravitational singularity #Hypersurface #Mathematical analysis #Mathematical physics #Mathematics #Null (SQL) #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Spacetime #gr-qc
paper · pdf · doi:10.1103/physrevd.65.084045
published as Phys.Rev. D65 (2002) 084045 · 26 pages, revtex4, 1 eps figure; matches version to appear in Phys. Rev. D (in press)
arxiv created 2002/03/22 · openalex publication_date 2002/04/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The gravitational collapse of an infinite cylindrical thin shell of generic matter in an otherwise empty spacetime is considered. We show that geometries admitting two hypersurface orthogonal Killing vectors cannot contain trapped surfaces in the vacuum portion of spacetime causally available to geodesic timelike observers. At asymptotic future null infinity, however, congruences of outgoing radial null geodesics become marginally trapped, due to the convergence induced by the shear caused by the interaction of a transverse wave component with the geodesics. The matter shell itself is shown to be always free of trapped surfaces, for this class of geometries. Finally, two simplified matter models are analytically examined. For one model, the weak energy condition is shown to be a necessary condition for collapse to halt; for the second case, it is a sufficient condition for collapse to be able to halt.