Bouncing Spheres in General Relativity

Abstract

I REPORT here an analysis recently completed of the radial adiabatic motion of spherically symmetric models of uniform density and isotropic pressure in general relativity. An appropriate form of the metric is with r and t being radial and time-like labels, respectively, and dots denoting differentiation with respect to t. At this stage a.(t) and b(t) are arbitrary functions of t, and suffix s referring to the surface of the model and ms being the mass of the model according to the external Schwarz-schild metric. It can readily be shown from this that where ds is the proper time of a co-moving observer on the surface of the model. Furthermore (with suffix c denoting the centre)