An approach to the quasi-equilibrium state of a self-gravitating system

Abstract

We propose an approach to find out when a self-gravitating system is in its quasi-equilibrium state. This approach is based on a comparison between two quantities identifying behavior of the system: a measure of interactions intensity and the area. The quasi-equilibrium state of such system is considered as a state when these quantities satisfy a local specific condition. As the first result, we obtain an equation which relates density and temperature for such a system in the non-relativistic classical limit. This equation is consistent with the TOV equation as an expectation.