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In this work we consider an isothermic relativistic kinetic gas under relativistic conditions, as a model for high center density galaxies. We apply the radius cutoff of the Emden type, in order to remove infinities. Numerically we find some theoretical configurations with very high values of masses concentrated in small volumes. Profiles of some thermodynamic quantities such as density, presure, will be independent from the choice of radius cutoff, whereas temperature and gravitational potential depend essentially on the cutoff value.