Dynamical instability of fluid spheres in the presence of a cosmological constant

TL;DR

This paper investigates how a cosmological constant affects the dynamical stability of relativistic fluid spheres, revealing that a large cosmological constant raises the critical adiabatic index required for stability.

Contribution

It generalizes the equations for radial oscillations of relativistic stars to include a cosmological constant and analyzes its impact on stability criteria.

Findings

A large cosmological constant increases the critical adiabatic index.

Derived bounds on the maximum cosmological constant for stability.

Stability conditions in Schwarzschild-de Sitter geometry.

Abstract

The equations describing the adiabatic, small radial oscillations of general relativistic stars are generalized to include the effects of a cosmological constant. The generalized eigenvalue equation for the normal modes is used to study the changes in the stability of the homogeneous sphere induced by the presence of the cosmological constant. The variation of the critical adiabatic index as a function of the central pressure is studied numerically for different trial functions. The presence of a large cosmological constant significantly increases the value of the critical adiabatic index. The dynamical stability condition of the homogeneous star in the Schwarzschild-de Sitter geometry is obtained and several bounds on the maximum allowable value for a cosmological constant are derived from stability considerations.