Dynamical Evolutions of Electrically Charged Proca Stars

TL;DR

This paper investigates the dynamical stability of charged Proca stars, revealing their potential evolution into black holes, stable states, or dispersal, based on perturbations and charge parameters.

Contribution

It provides the first detailed analysis of the dynamical stability and evolution of electrically charged Proca stars under perturbations.

Findings

Stable, unstable, and unbound regions identified in parameter space.

Unstable stars can collapse into Reissner–Nordström black holes.

Final states depend on binding energy and perturbation form.

Abstract

In a previous work we constructed different families of stationary electrically charged Proca stars characterized by a charge parameter $q$, by solving the Einstein--Maxwell--Proca system in spherical symmetry, and imposing a harmonic time dependence ansatz for the Proca field (Mio and Alcubierre, 2025). We showed that there is a critical value for the charge $q_c$ that corresponds to the value for which the Coulomb repulsion of the charged Proca field exactly cancels the Newtonian gravitational attraction, and we found that supercritical solutions can only exist for a limited range of charges above this critical value $q>q_c$. Here we study the dynamical stability properties of these charged Proca stars by adding a small but finite perturbation to the original stationary configurations, and then performing numerical evolutions while keeping the spherical symmetry. We show that, for any given family, the parameter space can be separated into three regions corresponding to gravitationally bound stable configurations, gravitationally bound unstable configurations, and gravitationally unbound unstable configurations. For the unstable configurations we follow the evolution in time in order to determine their final state, and find that this final state can be collapse to a charged Reissner--Nordstrom black hole, migration to a new state in the stable branch, or dispersion to infinity, depending on the value of the binding energy and the specific form of the perturbation.