Absence of trapped surfaces and singularities in cylindrical collapse

TL;DR

This paper demonstrates that cylindrical gravitational collapse with certain symmetries does not produce trapped surfaces or singularities, and explores conditions affecting collapse halting, with implications for understanding cosmic censorship.

Contribution

It shows that geometries with two hypersurface orthogonal Killing vectors cannot contain trapped surfaces in the vacuum region, and analyzes matter models affecting collapse outcomes.

Findings

No trapped surfaces in vacuum regions for these geometries

Outgoing null geodesics become marginally trapped at null infinity

Weak energy condition influences collapse halting conditions

Abstract

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.