Relativistic Gravitational Collapse of Cylindrical Dust

The gravitational collapse of a cylindrical thick shell of dust matter is investigated. A spacetime singularity forms at the symmetry axis and it is necessarily naked, i.e., observable in principle. We propose a physically reasonable boundary condition at the naked singularity to construct the solution including its causal future. This boundary condition enables us to construct the unique continuation of spacetime beyond the naked singularity and makes the dust shell pass through the naked singularity. When the cylindrical shell has left the symmetry axis away, the naked singularity disappears and regularity is recovered. We succeed in constructing numerical solutions with this feature. This result means that gravity produced by a cylindrical thick shell of dust is too weak to bind itself even if it forms the curvature singularity which is so strong as to satisfy the limiting focusing condition. As a result, this naked singularity is very gentle in the extended spacetime; the metric tensor is C even at the naked singularity and the extended spacetime is complete for almost all geodesics. This feature is also seen for singular hypersurfaces. Such an extended spacetime can be regarded as phenomenological in a sense that it is valid providing that the relevant microphysics length scale is sufficiently small compared to the scale of interest.