INITIAL-BOUNDARY VALUE-PROBLEM FOR THE SPHERICALLY SYMMETRICAL EINSTEIN EQUATIONS FOR A PERFECT FLUID

It is shown that for a given spherically symmetric distribution of a perfect fluid on a spacelike hypersurface with boundary and a given, time-dependent boundary pressure. there exists a unique, local-in-time solution of the Einstein equations. A Schwarzschild spacetime can be attached to the fluid body if and only if the boundary pressure vanishes. We assume a smooth equation of state for which the density and the speed of sound remain positive for vanishing pressure.