Stability of dense stellar clusters against relativistic collapse

Stability of dense stellar clusters against relativistic collapse is investigated by approximate methods, similar to the static criteria of stellar stability. The equilibrium models with Maxwellian distribution function with cutoff, studied by Zel'dovich & Podurets (ZP) (1965), have been considered. Three new methods for stability investigation are considered. They give only approximate results about the stability, because adiabatic perturbations of the collisionless Maxwellian model lead to complicated non-Maxwellian distribution, which cannot be written analytically. However, these results are more precise than those of ZP, obtained from consideration of the sequence of Maxwellian models with different temperature. The coincidence of the temperatures in the critical point, T = 0.223 mc^2 leads us to believe that these methods, although approximate, provide rather relatively good precision not worse than 0.001.