Gravitational Collapse

Abstract

THE stellar-like radio sources (‘quasars’), of which 3C48 and 3C273 are examples, appear to be objects with very small diameters yet the total energies of which lie in the range 10⁶⁰–10⁶¹ ergs. At the moment, the only source that has been imagined for the production of such high energies, is the Newtonian gravitational potential energy of a highly compressed mass. If a mass equal to some 10⁸ solar masses could be compressed into a sphere the diameter of which equalled that of the orbit of Pluto, a gravitational potential energy of the required order of magnitude would become available. During the past thirty years a number of authors have shown that a compression of this kind is predicted by Einstein's equations of general relativity. It is postulated that the only force acting is the gravitational self-attraction of the material, that the density is uniform throughout the spherical mass at each instant of time and that the pressure is always zero. The last condition implies that the material remains at the absolute zero of temperature throughout the collapse to a small volume. These assumptions lead to the conclusion that, for such zero-pressure configurations, the motion continues until a singular state is reached in which the volume occupied by the material tends to a zero value whereas its density becomes infinite. The time of collapse is very short: at best it occurs in a few hundreds of thousands of years, but it may also be over in a matter of weeks or days, depending on the initial conditions.