Abstract. Collisionless star clusters in dynamical equilibrium are of current interest in general relativity and astrophysics. A step-function distribution is chosen for star clusters. The corresponding equation of state is analogous to a Fermi-gas equation. These clusters are found to be pulsationally unstable for a central redshift ofZc ⩾ 0·54. Further, a model of clusters is developed in which the core has an extremely relativistic equation of state. These structures are unstable forZc ⩾ 2·55 when we use Chandrasekhar’s technique to study their pulsational stability.
