Relativistic Gas Spheres and Clusters of Point Masses with Arbitrarily Large Central Redshifts: can they BE Stable?

Recently Bisnovatyi-Kogan and Zel'dovich have constructed general-relativistic models of gas spheres and of collision less star clusters, for which the red shift from the center to infinity is arbitrarily large; and they have speculated that these particular models might be stable against small perturbations. In this paper we prove that the gas spheres are, indeed, stable-at least against radial perturbations. As for the clusters, we show that the most powerful techniques yet devised yield inconclusive results for stability. However, from the behavior of the clusters under scrutiny by those techniques, we believe that probably they are stable.