GRAVITATIONAL COLLAPSE OF AN INFINITE, CYLINDRICAL DUST SHELL

The evolution of an infinitely long, cylindrical shell of pressureless matter, which collapses because of its own gravitational pull, is studied analytically at late times and numerically for all times. The shell starts from rest and collapses in finite time, as seen by all observers, to form a naked singularity. The singularity is strong in the sense that observers riding on the shell experience, as they reach the singularity, an infinite net stretch parallel to the symmetry axis and an infinite net squeeze in the azimuthal direction. A strong burst of gravitational radiation, which is emitted just before the singularity forms, creates stretches and squeezes in opposite directions to those of the singularity itself. a squeeze along the symmetry axis and a stretch in the azimuthal direction. The numerical analysis gives a complete picture of the shell's motion during the collapse and of the evolution of the spacetime geometry and the emission and propagation of the gravitational wave burst.