Hydrodynamic Calculations of General-Relativistic Collapse

Abstract

The general-relativistic equations governing the motion of a large mass under the influence of its own gravitational field and its own pressure have been approximated by finite-difference equations. A spherically symmetric, co-moving frame of reference was used. The pressure was assumed to be zero at the outer boundary. Rest mass was assumed to be conserved and heat transfer by neutrinos, radiation, etc., was not taken into account. Numerical solutions were obtained on a computer for several simplified equations of state, chosen to bracket the behavior of stellar material in late stages of collapse, and several masses. The maximum stable masses obtained were of the same order of magnitude, but somewhat larger than the maximum stable masses calculated statically. The behavior of light signals, of the metric coefficients, and of the hydrodynamic quantities as functions of time is described for collapse past the Schwarzchild radius. Such collapse leads to regions where the surface area of concentric spheres decreases as the rest mass contained by the spheres increases.