Selfgravitating Gas Spheres in a Box and Relativistic Clusters: Relation   between Dynamical and Thermodynamical Stability
  We derive a variational principle for the dynamical stability of a cluster as a gas sphere in a box. Newtonian clusters are always dynamically stable and, for relativistic clusters, the relation between dynamical and thermodynamical instabilities is analyzed. The boundaries between dynamically and thermodynamically stable and unstable models are found numerically for relativistic stellar systems with different cut off parameters. A criterion based on binding energy curve is used for determination of the boundary of dynamical stability. 
Gennady S. Bisnovatyi-Kogan, Marco Merafina