SUFFICIENT CONDITIONS FOR APPARENT HORIZONS IN SPHERICALLY SYMMETRICAL INITIAL DATA

We establish sufficient conditions for the appearance of both apparent horizons and singularities in spherically symmetric initial data when spacetime is foliated extrinsically. Let M and P be, respectively, th e total material energy and the total material current contained in so me ball of radius l. Suppose that the dominant energy condition is sat isfied. We show that if M - P greater than or equal to l then the regi on must possess a future apparent horizon for some nontrivial closed s ubset of such gauges. The same inequality holds on a larger subset of gauges but with a larger constant of proportionality which depends wea kly on the gauge. This work extends substantially both our joint work on moment of time symmetry initial data as well as the work of Bizon, Malec, and O Murchadha on a maximal slice. [S0556-2821(97)00524-9].