A multi-term trial function stability analysis of isotropic relativistic star clusters

A multi-term trial function technique is developed for studying the dynamic stability of isotropic relativistic star clusters by using the variational principle originated by Ipser and Thorne (1968). The technique is applied ton=4 polytropic clusters, and low-temperature isothermal clusters. These two types of cluster have pronounced core-halo structures and they have both proved difficult to analyse with single-term trial function methods. Then=4 polytropic clusters are proved to be dynamically unstable if their central redshifts are greater thanz _c=0.412. This is quite close to the point on their sequence withz _c=0.41, where their fractional binding energy peaks. Strong evidence is obtained that all isothermal clusters with no dispersion in the stellar rest mass become dynamically unstable near the region where their fractional binding energy peaks, and that none of these clusters is dynamically stable if their central redshift exceedsz _c0.53.