Nonstatic Solutions of Einstein's Field Equations for Spheres of Fluids Radiating Energy

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 $r\le a\left(t\right)\mathrm{}$, an ever-expanding zone of pure radiation for $a\left(t\right)\mathrm{}\le r\le b\left(t\right)\mathrm{}$ and empty space beyond $r=b\left(t\right)\mathrm{}$. Since $\frac{\mathrm{db}\left(t\right)\mathrm{}}{\mathrm{dt}}$ is almost equal to 1 and $\frac{\mathrm{da}\left(t\right)\mathrm{}}{\mathrm{dt}}$ is negative, the solutions obtained represent contracting distributions, but the contraction is not gravitational because $\frac{m}{r}$ is a constant on the boundary $r=a\left(t\right)\mathrm{}$, $m$ 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.