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Families of steady states of the spherically symmetric Einstein-Vlasov systemare constructed, which are parametrized by the central redshift. It is shownthat as the central redshift tends to zero, the states in such a family arewell approximated by a steady state of the Vlasov-Poisson system, i.e., aNewtonian limit is established where the speed of light is kept constant as itshould be and the limiting behavior is analyzed in terms of a parameter whichis tied to the physical properties of the individual solutions. This result isthen used to investigate the stability properties of the relativistic steadystates with small redshift parameter in the spirit of recent work by the sameauthors, i.e., the second variation of the ADM mass about such a steady stateis shown to be positive definite on a suitable class of states.

On the small redshift limit of steady states of the spherically symmetric Einstein-Vlasov system and their stability