On the behavior of non-static models of the universe when the cosmological term is omitted

Abstract

If the cosmological term in the equations of relativistic mechanics is set equal to zero, it has been shown by Einstein that a non-static model of the universe filled with a homogeneous distribution of incoherent matter would expand to a maximum volume and then start contracting. This, however, is a very special model of the universe filled with a highly simplified fluid, and subjected to changes which can be shown to be thermodynamically reversible; and it has recently been pointed out by one of the present authors that we can also expect a similar expansion to a maximum volume with much more general models of the universe allowing irreversible as well as reversible changes in the fluid filling the model. The present article gives a somewhat detailed analysis of the behavior of a wide class of non-static models of the universe when the cosmological term is set equal to zero, and shows that we may expect a continued succession of expansions and contractions without reference to the reversible or irreversible nature of the processes taking place in the fluid filling the model. The bearings of this finding on the problems of relativistic thermodynamics, which have already been treated by one of the present authors, are again noted.