Cylindrically symmetric models of gravitational collapse to black holes: a short review

We survey results about exact cylindrically symmetric models of gravitational collapse in General Relativity. We focus on models which result from the matching of two spacetimes having collapsing interiors which develop trapped surfaces and vacuum exteriors containing gravitational waves. We collect some theorems from the literature which help to decide a priori about eventual spacetime matchings. We revise, in more detail, some toy models which include some of the main mathematical and physical issues that arise in this context, and compute the gravitational energy flux through the matching boundary of a particular collapsing region. Along the way, we point out several interesting open problems.The author thanks R. Vera for his careful reading of the manuscript and for his many suggestions and references which greatly improved the paper; J. Senovilla for providing reference;48 the organisers of the VII Black Hole Workshop; FCT project CERN/FP/123609/2011; CMAT, Univ. Minho, through FEDER funds COMPETE and FCT funds Est-OE/MAT/UI0013/2014