Radial stability analysis of the continuous pressure gravastar

TL;DR

This paper investigates the radial stability of continuous pressure gravastars by deriving their equations of state, solving perturbation equations, and identifying parameter regimes that ensure stability, thus confirming their potential viability as astrophysical objects.

Contribution

It provides a comprehensive stability analysis of continuous pressure gravastars, including derivation of equations of state and eigenvalue solutions for radial pulsations, extending previous axial stability work.

Findings

Existence of stable parameter sets for gravastars.

Identification of a critical extremum in the central energy density curve.

Completion of the stability analysis for the continuous pressure gravastar model.

Abstract

Radial stability of the continuous pressure gravastar is studied using the conventional Chandrasekhar method. The equation of state for the static gravastar solutions is derived and Einstein equations for small perturbations around the equilibrium are solved as an eigenvalue problem for radial pulsations. Within the model there exist a set of parameters leading to a stable fundamental mode, thus proving radial stability of the continuous pressure gravastar. It is also shown that the central energy density possesses an extremum in rho_c(R) curve which represents a splitting point between stable and unstable gravastar configurations. As such the rho_c(R) curve for the gravastar mimics the famous M(R) curve for a polytrope. Together with the former axial stability calculations this work completes the stability problem of the continuous pressure gravastar.