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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 vaccum 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.
We investigate a class of cylindrically symmetric inhomogeneous $Lambda$-dust spacetimes which have a regular axis and some zero expansion component. For $Lambda e 0$, we obtain new exact solutions to the Einstein equations and show that they are uni
We match collapsing inhomogeneous as well as spatially homogeneous but anisotropic spacetimes to vacuum static exteriors with a negative cosmological constant and planar or hyperbolic symmetry. The collapsing interiors include the inhomogeneous solut
We derive the matching conditions between FLRW and generalised Vaidya spacetimes with spherical, planar or hyperbolic symmetry, across timelike hypersurfaces. We then construct new models of gravitational collapse of FLRW spacetimes with a negative c
We introduce a systematic and direct procedure to generate hairy rotating black holes by deforming a spherically symmetric seed solution. We develop our analysis in the context of the gravitational decoupling approach, without resorting to the Newman
We investigate an infinitesimally thin cylindrical shell composed of counter-rotating dust particles. This system was studied by Apostolatos and Thorne in terms of the C-energy for a bounded domain. In this paper, we reanalyze this system by evaluati