Thermodynamic stability of relativistic stellar clusters

Equilibrium configurations of isothermal relativistic stellar clusters with truncated isotropic Maxwell-Boltzmann distribution of energies have been studied. An argument is given, showing that the energy cutoff should be equal to the gravitochemical potential as seen from infinity. Solutions of Einstein's equations are obtained for a wide range of values of temperature and chemical potential as seen from infinity. Conditions of stability are determined by thermodynamic criteria. It is shown that the (temperature, chemical potential) -plane contains two possible regions of stability in the limits of our calculations. One region is related to the stable configurations found by dynamical means. The second zone is new and is associated with values of the central redshift ranging from 1 to 4