Dynamics of Fluid Spheres of Uniform Density

The adiabatic collapse of spheres of uniform density made up of perfect fluids either electrically neutral or charged has been studied. A set of field equations equivalent to Einstein's field equations are derived in terms of the energy-momentum tensor. With the help of these equations, the following theorems for perfect fluid spheres have been established: (1) For the gravitational collapse or bounce of a homogeneous sphere of perfect fluid the only motions possible are shear-free, uniform contraction or expansion. (2) For a charged fluid sphere embedded in empty space the conditions $\rho =\rho \mathrm{}\left(t\right)\mathrm{}$ and $\dot{\lambda }=\dot{\mu }$ are inconsistent in the sense that either the solutions are static or matter is uncharged.