Dynamical stability of fluid spheres in spacetimes with a nonzero cosmological constant

TL;DR

This paper investigates how a nonzero cosmological constant affects the stability of fluid spheres, showing that a repulsive cosmological constant increases the critical adiabatic index and decreases the critical radius for instability.

Contribution

It derives the Sturm-Liouville eigenvalue equation for radial oscillations in spacetimes with a cosmological constant and analyzes stability criteria for specific fluid configurations.

Findings

A positive cosmological constant raises the critical adiabatic index.

A positive cosmological constant decreases the critical radius for instability.

The analysis applies to uniform density and polytropic spheres.

Abstract

The Sturm-Liouville eigenvalue equation for eigenmodes of the radial oscillations is determined for spherically symmetric perfect fluid configurations in spacetimes with a nonzero cosmological constant and applied in the cases of configurations with uniform distribution of energy density and polytropic spheres. It is shown that a repulsive cosmological constant rises the critical adiabatic index and decreases the critical radius under which the dynamical instability occurs.