Electrically Charged Proca Stars

TL;DR

This paper constructs and analyzes charged Proca star solutions in spherical symmetry, revealing a critical charge where Coulomb repulsion balances gravity, and identifying stability limits related to charge and binding energy.

Contribution

It introduces the first detailed construction of charged Proca stars, exploring their properties, stability, and the critical charge where forces balance.

Findings

Existence of a critical charge $q_c$ where Coulomb repulsion balances gravity.

Supercritical solutions exist but are likely unstable.

Bound states with negative binding energy only occur for subcritical charges.

Abstract

We consider self-gravitating stationary configurations of a charged massive complex Proca field, also known as charged Proca stars, in the particular case of spherical symmetry. We first present a general 3+1 decomposition of the Einstein--Maxwell--Proca system, starting from the action and field equations. We then restrict our system to the case of spherical symmetry and, after imposing a harmonic time dependence ansatz for the Proca field, we construct families of charged Proca stars for different values of the charge parameter $q$, and different values of the central Proca scalar potential $\varphi$. In a similar way to the case of scalar boson stars, one can define a critical charge $q=q_c$ that corresponds to the value for which the Coulomb repulsion of the charged Proca field exactly cancels their newtonian gravitational attraction. We find that supercritical solutions can exist for a limited range of charges above the critical value $q>q_c$. We also consider the binding energy $E_B$ for the different families of solutions, and find that gravitationally bound solutions such that $E_B<0$ can only exist for subcritical charges such that $q<q_c$, indicating that our supercritical solutions are probably dynamically unstable against perturbations.