Statistical Mechanics of the Self-Gravitating Gas: Thermodynamic Limit, Unstabilities and Phase Diagrams

Abstract

We show that the self-gravitating gas at thermal equilibrium has an infinite volume limit in the three ensembles (GCE, CE, MCE) when (N, V) -> infty, keeping N/V^{1/3} fixed, that is, with eta = G m^2 N/[ V^{1/3} T] fixed. We develop MonteCarlo simulations, analytic mean field methods (MF) and low density expansions. We compute the equation of state and find it to be locally p(r) = T rho_V(r), that is a local ideal gas equation of state. The system is in a gaseous phase for eta < eta_T = 1.51024...and collapses into a very dense object for eta > eta_T in the CE with the pressure becoming large and negative. The isothermal compressibility diverges at eta = eta_T. We compute the fluctuations around mean field for the three ensembles. We show that the particle distribution can be described by a Haussdorf dimension 1 < D < 3.

12 pages, Invited lecture at `Statistical Mechanics of Non-Extensive Systems', Observatoire de Paris, October 2005, to be published in a Special issue of `Les Comptes rendus de l'Acade'mie des sciences', Elsevier

References in corpus (4)

• The self-gravitating gas in the presence of dark energy
• The Cluster Expansion for the Self-Gravitating gas and the Thermodynamic Limit
• The Self-Gravitating Gas in the Presence of Dark Energy: Monte-Carlo Simulations and Stability Analysis
• Statistical Mechanics of the self-gravitating gas: thermodynamic limit, phase diagrams and fractal structures

Cited by in corpus (3)

• Density profiles of a self-gravitating lattice gas in one, two, and three dimensions
• Semiclassical and Quantum Black Holes and their Evaporation, de Sitter and Anti-de Sitter Regimes, Gravitational and String Phase Transitions
• Self-Gravitating Phase Transitions: Point Particles, Black Holes and Strings