Nonstatic solutions of Einstein's field equations for spheres of fluids radiating energy

Abstract

The energy tensor for a mixture of matter and outflowing radiation is derived, and a set of equations following from Einstein's field equations are written down whose solutions would represent nonstatic radiating spherical distributions. A few explicit analytical solutions are obtained, which describe a distribution of matter and outflowing radiation for r≤ a(t), an ever-expanding zone of pure radiation for a(t)≤ r≤ b(t) and empty space beyond r=b(t). Since db(t)/dt is almost equal to 1 and da(t)/dt is negative, the solutions obtained represent contracting distributions, but the contraction is not gravitational because m/r is a constant on the boundary r=a(t), m being the mass. The contraction is a purely relativistic effect, the corresponding newtonian distributions being equilibrium distributions. It is hoped that the scheme developed here will be useful in working out solutions which would help in a clear understanding of the initial or the final stages of stellar evolution.