Oscillatory behavior of charge-matter fluids with e/m>G/sup 1/2/

It is shown that the exact solutions of the spherically symmetric time-dependent pressure-free Einstein-Maxwell equations with external $\frac{e}{m}>G^{\frac{1}{2}}$ allow steady-state oscillatory behavior but only under the same conditions that were found previously to be necessary for equilibrium in the static case, namely (1) that a divergence exists in g₄₄ at the center, (2) that the matter density is negative, at least near the center, and (3) that the ratio of charge to matter density is not constant.