Stable Gravastars: Guilfoyle's electrically charged solutions

TL;DR

This paper constructs a charged gravastar model using Guilfoyle's solutions, matching de Sitter interior to Reissner-Nordström exterior, and analyzes stability and physical properties to propose a compelling alternative to black holes.

Contribution

It introduces a new charged gravastar model based on Guilfoyle's solutions with a specific energy density assumption, avoiding horizons and enabling stability analysis.

Findings

Certain parameter ranges avoid horizon formation.

Stable, non-horizon gravastar configurations are possible.

Physical and geometrical properties support the viability of the model.

Abstract

Compelling alternatives to black holes, namely, gravitational vacuum star ({\it gravastar}) models, the multilayered structure compact objects, have been proposed to avoid a number of theoretical problems associated with event horizons and singularities. In this work, we construct a spherically symmetric thin-shell charged gravastar model where the vacuum phase transition between the de Sitter interior and the external Reissner--Nordstr$\ddot{\text{o}}$m spacetime (RN) are matched at a junction surface, by using the cut-and-paste procedure. Gravastar solutions are found among the Guilfoyle exact solutions where the gravitational potential $W^2$ and the electric potential field $\phi$ obey a particularly relation in a simple form $ a\left(b-\epsilon \phi \right)^2 +b_1$, where $a$, $b$ and $b_1$ being arbitrary constants. The simplest ansatz of Guilfoyle's solution is implemented by the following assumption: that the total energy density $8\pi \rho_m+\frac{Q^2}{ r^4}$ = constant, where $Q(r)$ is the electric charge up to a certain radius $r$. We show that, for certain ranges of the parameters, we can avoid the horizon formation, which allows us to study the linearized spherically symmetric radial perturbations around static equilibrium solutions. To lend our solution theoretical support, we also analyze the physical and geometrical properties of gravastar configurations.