Relative chaos in gravitating systems with massive centre

A geometric method, using the Ricci (or mean) curvature of the Lagrangian (configuration) manifold, is used to study the relative instability of evolving $N$-body gravitating systems with massive centres. The performed numerical experiments show that the Ricci curvature decreases with the increase in central concentration, thus indicating an increasing instability for systems with massive centre --- either in the form of a point mass or a core formed during the evolution of single and multimass systems. Simulations of such systems do indeed suggest that they have faster gravothermal evolution than less concentrated ones.