Comment on "Absence of trapped surfaces and singularities in cylindrical collapse"

TL;DR

This paper critiques a previous study on cylindrical gravitational collapse, demonstrating that trapped surfaces can indeed form, contrary to earlier claims, by redefining their criteria and providing explicit counterexamples.

Contribution

The authors correct the definition of trapped surfaces in cylindrical spacetimes and show that previous claims of their non-existence are incorrect through explicit examples.

Findings

Gon extquotesingle c extquotesingle alves' criterion is incorrect.

Trapped surfaces can form in cylindrical vacuum spacetimes.

Explicit example confirms the existence of trapped surfaces.

Abstract

Recently, the gravitational collapse of an infinite cylindrical thin shell of matter in an otherwise empty spacetime with two hypersurface orthogonal Killing vectors was studied by Gon\c{c}alves [Phys. Rev. {\bf D65}, 084045 (2002).]. By using three "alternative" criteria for trapped surfaces, the author claimed to have shown that {\em they can never form either outside or on the shell, regardingless of the matter content for the shell, except at asymptotical future null infinite}. Following Penrose's original idea, we first define trapped surfaces in cylindrical spacetimes in terms of the expansions of null directions orthogonal to the surfaces, and then show that the first criterion used by Gon\c{c}alves is incorrect. We also show that his analysis of non-existence of trapped surfaces in vacuum is incomplete. To confirm our claim, we present an example that is a solution to the vacuum Einstein field equations and satisfies all the regular conditions imposed by Gon\c{c}alves. After extending the solution to the whole spacetime, we show explicitly that trapped surfaces exist in the extended region.