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Published online by Cambridge University Press: 14 August 2015
Relativistic stellar-dynamical systems and their possible occurrence in nature are discussed. Features of the equilibrium models that have been constructed for spherical star clusters in general relativity are delineated. The results of studies of the stability of relativistic spherical clusters are reviewed. It is noted that the results, while not conclusive, indicate that realistic spherical clusters are stable against gravitational collapse if their central redshifts zc ≲ 0.55 and unstable if zc ≳ 0.55. More work is needed on this and other problems.