A dynamical condition for a relativistic galaxy cluster model

In an attempt to give a coherent interpretation of the secondary maximum in the density distribution of clusters an approximate metric tensor proposed by other authors is used with the purpose of building a relativistic generalization of the isothermal models of galaxy clusters. Although such a generalization gives rise to oscillations in the density distribution, the quantitative agreement with the observational data is unsatisfactory. The analysis of the metric tensor used brings out the points (i) the approximation on which the metric is based is not suitable for describing an actual galaxy and (ii) the dynamical conditions of clusters require inclusion of a cosmological expansion, and of anisotropic distribution function in the phase-space. (Auth.)