The steepest descent technique and stellar equilibrium statistical mechanics. II. Relativistic clusters in a box.
Abstract
Thermodynamic equilibrium and stability conditions are investigated for relativistic configurations of a model of rotating star clusters containing particles of equal mass that interact only through gravitation. A functional integral expression for the microcanonical entropy of an axisymmetric system of particles confined to an axisymmetric volume of arbitrary shape is formulated which is a relativistic generalization of an exact expression previously obtained for Newtonian systems. A steepestdescent technique is then used to calculate the meanfield value of the entropy for axisymmetric configurations of particles; the contribution from quadratic fluctuations of the mean field is also computed. A set of global and local necessary and sufficient conditions for stability to axisymmetric perturbations is obtained, the local stability conditions are analyzed, and their explicit form is determined for the case of spherically symmetric mean fields plus fluctuations that are arbitrary except for the exclusion of convective flows. A formal connection with the Newtonian limit is established.
 Publication:

The Astrophysical Journal Supplement Series
 Pub Date:
 February 1977
 DOI:
 10.1086/190429
 Bibcode:
 1977ApJS...33..251K
 Keywords:

 Star Clusters;
 Statistical Mechanics;
 Steepest Descent Method;
 Stellar Models;
 Dynamic Stability;
 Relativity;
 Stellar Rotation;
 Thermodynamic Equilibrium;
 Astrophysics