Cylindrical Dust Collapse in General Relativity: Toward Higher Dimensional Collapse

Motivated by possible spindle naked singularity formation in prolate collapse, we investigate the dust collapse in cylindrically symmetric spacetime. First, possible singularity avoidance property of the maximal time slicing in cylindrically symmetric spacetime is investigated. It is found both analytically and numerically that the maximal time slicing never has that property and that the lapse function decreases only slowly and hits a singularity in cylindrically symmetric spacetime. We propose a new kind of time slice which may be suitable to investigate the formation of a cylindrical singularity. Second taking into account these results, dust collapse is investigated numerically in order to see the role of gravitational waves during the gravitational collapse leading to a naked singularity. We find negligible gravitational wave emission during the free fall time. This is consistent with Shapiro-Teukolsky claim that neglibible gravitational waves are emitted in prolate collapse of collisionless particles. The implications of these results for axisymmetric collapse, especially for prolate collapse, are also discussed.