Stable Gravastars: Guilfoyle'S Electrically Charged Solutions

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