  The radial collapse of a homogeneous disk of collisionless particles can be
solved analytically in Newtonian gravitation. To solve the problem in general
relativity, however, requires the full machinery of numerical relativity. The
collapse of a disk is the simplest problem that exhibits the two most
significant and challenging features of strong-field gravitation: black hole
formation and gravitational wave generation. We carry out dynamical
calculations of several different relativistic disk systems. We explore the
growth of ring instabilities in equilibrium disks, and how they are suppressed
by sufficient velocity dispersion. We calculate wave forms from oscillating
disks, and from disks that undergo gravitational collapse to black holes.
Studies of disk collapse to black holes should also be useful for developing
new techniques for numerical relativity, such as apparent horizon boundary
conditions for black hole spacetimes.
