Dimensionally regularized Boltzmann-Gibbs statistical mechanics and two-body Newton's gravitation

M. C. ROCCA; A. PLASTINO; D.J. ZAMORA; G.L. FERRI

CABA

Conferencia; StatPhys 27- International Conference on Statistical Physics; 2019

IUPAP- International Union of Pure and Applied Physics

It is believed that the canonical gravitational partition function Z associated to the classical Boltzmann?Gibbs (BG) distribution cannot be constructed because the integral needed for building up Z includes an exponential and thus diverges at the origin [1,2]. We show here that, by recourse to the analytical extension (AE) treatment obtained by Gradshteyn and Rizhik, and the dimensional regularization approach of Bollini and Giambiagi?s (DR), one can indeed obtain finite gravitational results employing the BG distribution.This kind of systems, call selfgravitational systems, has interesting features, like negative specific heats, that we are interested in calculate but no one could do it because of the divergence of the integrals.