Spherically Symmetric Motions in General Relativity

Abstract

I HAVE recently obtained certain exact solutions of Einstein's equations of general relativity which, so far as I can trace, have not been noticed before. They refer to a spherically symmetric mass of material in radial motion which may either be collapsing on to the central point (gravitational collapse) or be exploding from that point (spherical blast). The solutions are determined from three general conditions: (1) from a certain pre-assigned form for the coefficients of the metric; (2) from the existence of co-moving co-ordinates; (3) from the assumption that the stress is spatially isotropic. The results have analogies with the spherical blast waves of classical gas-dynamics¹, but with the additional feature that the gravitational self-attraction of the material is a controlling element of the motion. A by-product of the investigation is the discovery of the class of solutions of Einstein's equations to which belongs a particular case² obtained in 1933 by a different method.