Multipolar Proca stars: electric, magnetic and hybrid solitons

TL;DR

This paper introduces new regular, asymptotically flat solitons in the Einstein--Proca model, including electric, magnetic, and hybrid types, and analyzes their stability and evolution.

Contribution

It constructs novel multipolar Proca star solutions, including hybrid configurations with unique properties, expanding the landscape of known solitons in the Einstein--Proca system.

Findings

Electric Proca stars include the spherical case as $ ext{l}=0$.

Magnetic and hybrid solutions exhibit non-trivial angular momentum properties.

Hybrid solutions can be unstable, decaying into other Proca star configurations or collapsing into black holes.

Abstract

We construct new families of everywhere regular, asymptotically flat solitons in the Einstein--Proca model, obtained as self-gravitating continuations of flat-spacetime (singular) Proca multipoles. First we consider static and axially symmetric solutions, organized by a multipole number $\ell$. Two distinct classes arise: electric-type configurations, which include the spherical Proca stars as the $\ell=0$ case, and magnetic-type configurations, which have no spherical counterpart and start at $\ell=1$. Then we construct hybrid solutions as nonlinear superpositions of electric and magnetic multipoles. These have non-vanishing local angular momentum density but vanishing total angular momentum, and in some cases have no north-south $\mathbb{Z}_2$-symmetry. By performing dynamical evolutions of Proca stars in the new magnetic and hybrid sectors, we show they are unstable, decaying to the (static) prolate Proca stars or the (stationary) spinning Proca stars, previously identified as dynamically robust, electric sector configurations. In some cases, they can also collapse into a black hole.