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

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 Goncalves [Phys. Rev. D 65, 084045 (2002)]. By using three alternative criteria for trapped surfaces, the author claimed to have shown that they can never form either outside or on the shell, regardless of the matter content for the shell, except at asymptotical future null infinity. 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 Goncalves is incorrect. We also show that his analysis of nonexistence of trapped surfaces in the 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 Goncalves. After extending the solution to the whole spacetime, we show explicitly that trapped surfaces exist in the extended region.