Gravastar Solutions with Continuous Pressures and Equation of State

TL;DR

This paper presents a continuous, anisotropic gravastar model connecting de Sitter and Schwarzschild spacetimes, deriving a polytropic equation of state, and demonstrating stability and adherence to energy conditions.

Contribution

It introduces a novel continuous stress-energy tensor approach for gravastars, replacing multilayered structures with anisotropic fluid models and deriving a stable, energy-condition-compliant solution.

Findings

Solutions satisfy expected gravastar conditions

Energy conditions are obeyed

Stability under axial perturbations is confirmed

Abstract

We study the gravitational vacuum star (gravastar) configuration as proposed by other authors in a model where the interior de Sitter spacetime segment is continuously extended to the exterior Schwarzschild spacetime. The multilayered structure in previous papers is replaced by a continuous stress-energy tensor at the price of introducing anisotropy in the (fluid) model of the gravastar. Either with an ansatz for the equation of state connecting the radial $p_r$ and tangential $p_t$ pressure or with a calculated equation of state with non-homogeneous energy/fluid density, solutions are obtained which in all aspects satisfy the conditions expected for an anisotropic gravastar. Certain energy conditions have been shown to be obeyed and a polytropic equation of state has been derived. Stability of the solution with respect to possible axial perturbation is shown to hold.