Statistical Mechanics of planar stellar systems: Solving divergences in self-gravitational systems

It is believed that the canonical gravitational partition function associated with the two-body interacting Newton's gravitation cannot be constructed because the concomitant integral is exponentially divergent. We showed previously that one can indeed obtain finite gravitational results employing both the Gibbs-Boltzmann distribution and Tsallis' one, by recourse to the analytical extension treatment and the generalization of Bollini and Giambiagi's dimensional regularization. We deal here with a model of disc galaxy with a supermassive black hole at its center. Some interesting and coherent results emerge: i-an upper bound in the temperature, ii-the specific heat is negative, iii-the limit of the specific heat when the mass of the black-hole tends to zero is -k(B), iv-the third law of thermodynamics is violated, and v-the gravothermal catastrophe is avoided if the number of constituents of a surrounding halo is equal or less than the number of stars in the galaxy. (C) 2020 Elsevier B.V. All rights reserved.