Gravitational collapse of marginally bound spheroids: Initial conditions

A method is given for solving the general relativistic initial-value problem in the case of some collapsing, marginally bound, nonrotating configurations. Explicit solutions are found for oblate and prolate spheroids. Maximum efficiency limits for subsequent gravitational radiation are 2.5% (oblate) and 3.4% (prolate) for spheroids so compact that they lie within an apparent horizon on the initial slice.