Isothermal spheres from grand partition functions in nonextensive statistical mechanics

TL;DR

This paper analytically explores isothermal spheres within nonextensive statistical mechanics, deriving their equations from the grand partition function and examining how nonextensivity affects their stability, especially in dense regions.

Contribution

It introduces a new analytical framework for isothermal spheres using Tsallis statistics and investigates the impact of nonextensive parameters on their stability.

Findings

Nonextensive effects are significant in dense core regions.

Stability of relativistic isothermal spheres depends on the Tsallis q parameter.

Derived equations extend classical models to nonextensive contexts.

Abstract

We analytically study isothermal spheres in the light of nonextensive statistical mechanics. The equations for the isothermal spheres are derived from the grand partition function of the gravitating particle system in the Tsallis statistical mechanics. The effect of nonextensive statistics appears in relatively dense state, which appears at the center of the isothermal sphere. The stability of the isothermal sphere in the general relativistic system is found to be sensitive to the parameter q in the Tsallis statistics.