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

ZAMORA, D.J.; ROCCA, M.C.; PLASTINO, A.

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2020

0378-4371

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.