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

TL;DR

This paper introduces a method to determine when a self-gravitating system reaches a quasi-equilibrium state by balancing interaction measures and system area, deriving a density-temperature relation consistent with the TOV equation.

Contribution

It presents a novel approach to identify quasi-equilibrium in self-gravitating systems using interaction and area measures, resulting in a new density-temperature relation.

Findings

Derived an equation relating density and temperature in non-relativistic limit.

Established the consistency of this equation with the TOV equation.

Proposed a criterion for quasi-equilibrium based on interaction-area balance.

Abstract

We propose an approach to find out when a self-gravitating system is in a 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. Gravitational scattering cross section of the system, defined by using the two-particle scattering cross section formula, is considered as the measure of interactions intensity here. A quasi-equilibrium state of such system is considered as a state when there is a balance between these two quantities. As a 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 expected.