The Weyl tensor and equilibrium configurations of self-gravitating fluids

TL;DR

This paper establishes a link between the Weyl tensor's variation and the equilibrium state of spherically symmetric self-gravitating fluids, providing a criterion for equilibrium conditions.

Contribution

It introduces a new necessary and sufficient condition involving the Weyl tensor for the equilibrium of spherically symmetric fluid distributions.

Findings

Weyl tensor variation characterizes equilibrium states

Two specific cases where the condition does not apply

Provides a criterion for quasi-equilibrium states

Abstract

It is shown that (except for two well defined cases), the necessary and sufficient condition for any spherically symmetric distribution of fluid to leave the state of equilibrium (or quasi-equilibrium), is that the Weyl tensor changes with respect to its value in the state of equilibrium (or quasi-equilibrium).