The Role of Core in the Instability of Spherical Gravitating Systems

TL;DR

This paper investigates how the core's size influences the dynamical instability of spherical gravitating systems using Ricci curvature, revealing that the core can either stabilize or destabilize the system depending on its radius.

Contribution

It introduces a novel analysis of core effects on system instability using Ricci curvature, contrasting with the traditional focus on central mass influence.

Findings

Core size can both increase and decrease system instability.

Ricci curvature effectively measures dynamical instability.

Core behavior differs from that of a central mass.

Abstract

We study the dynamical instability in spherical gravitating systems with core using the Ricci curvature criterion. By means of numerical estimations of the Ricci curvature for static N-body systems, it is shown that the core can both, increase and decrease the degree of instability in the system. This behavior is determined by the radius of the core and differs from the role of a central mass.