Absence of trapped surfaces and singularities in cylindrical collapse

Details Absence of trapped surfaces and singularities in cylindrical collapse Absence of trapped surfaces and singularities in cylindrical collapse

2002-02-12

arxiv.org/abs/gr-qc/0202042v2

Phys.Rev. D65 (2002) 084045

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 pages, revtex4, 1 eps figure; matches version to appear in Phys. Rev. D (in press)

Scientific paper

10.1103/PhysRevD.65.084045

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 convergence induced by 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.

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