The Role of Core in the Instability of Spherical Gravitating Systems

We study the dynamical instability in spherical gravitating systems with core using the Ricci curvature criterion. By means of numerical estimations of the Ricci curvature for static N-body systems, it is shown that the core can both, increase and decrease the degree of instability in the system. This behavior is determined by the radius of the core and differs from the role of a central mass.