A method for calculating the space-time metric inside a collapsing or expanding sphere

A class of solutions of Einstein's field equations is found in which the quantities can be expressed as power series in r. Using null coordinates it is shown that the spacetime metric inside a spherically symmetric distribution of matter can be calculated to any degree of accuracy by evaluating the terms in the power series step by step, provided we know the central density, _O,as a function of time, and the equation of state in the form p=f(), f() being a function analytic at _O.The method is found to be applicable to all cases met with in nature.Presented at the International Conference on Gravitation and Relativity, Copenhagen, July 1971.