Time-Dependent Internal Solutions for Spherically Symmetrical Bodies in General Relativity: I. Adiabatic Collapse

The gravitational collapse of a spherically symmetrical distribution of matter, following an initial non-zero velocity distribution, is investigated on the basis of Einstein's field equations for the adiabatic (radiationless) case with a non-vanishing internal pressure gradient. In particular, it is shown that, if the density is uniform throughout the body at each instant (and so is a function of time only) and if the body continually contracts, it must, as in the pressure-free case, collapse to a point-singularity of infinite density in a finite time, as reckoned by a co-moving observer. To an external observer, the body would appear to contract asymptotically to its gravitational radius. The consequences of relaxing the adiabatic condition will be considered in a later paper.