  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.
