Nonlinear stability analysis of ℓ -Proca stars

Vector boson stars, also known as Proca stars, exhibit remarkable dynamical robustness, making them strong candidates for potential astrophysical exotic compact objects. In search of theoretically well-motivated Proca star models, we recently introduced the -Proca star, a multifield extension of the spherical Proca star, whose (2+1) constitutive fields have the same time and radial dependence, and their angular structure is given by all the available spherical harmonics for a fixed angular momentum number . In this work, we conduct a nonlinear stability analysis of these stars by numerically solving the Einstein- (multi-, complex) Proca system for the case of =2, which are formed by five constitutive independent, complex Proca fields with $m=0,|1|$, and $|2|$. Our analysis is based on long-term, fully nonlinear, three-dimensional numerical-relativity simulations without imposing any symmetry. We find that (=2)-Proca stars are unstable throughout their entire domain of existence. In particular, we highlight that less compact configurations dynamically lose their global spherical symmetry, developing a nonaxisymmetric m=4 mode instability and a subsequent migration into a new kind of multifield Proca star formed by fields with different angular momentum number, =1 and =2, that we identify as unstable multi--Proca stars.