# Non-linear dynamics of spinning bosonic stars: formation and stability

## TL;DR

This study uses numerical simulations to compare the formation and stability of spinning bosonic stars made of scalar and vector fields, revealing distinct stability behaviors and potential implications for astrophysical objects.

## Contribution

It provides the first detailed numerical analysis of the non-linear dynamics and stability of spinning bosonic stars, highlighting differences between scalar and Proca (vector) cases.

## Key findings

- Scalar boson stars are unstable and eject angular momentum.
- Proca stars are stable and resist large perturbations.
- Formation of scalar stars involves transient states and instabilities.

## Abstract

We perform numerical evolutions of the fully non-linear Einstein-(complex, massive)Klein-Gordon and Einstein-(complex)Proca systems, to assess the formation and stability of spinning bosonic stars. In the scalar/vector case these are known as boson/Proca stars. Firstly, we consider the formation scenario. Starting with constraint-obeying initial data, describing a dilute, axisymmetric cloud of spinning scalar/Proca field, gravitational collapse towards a spinning star occurs, via gravitational cooling. In the scalar case the formation is transient, even for a non-perturbed initial cloud; a non-axisymmetric instability always develops ejecting all the angular momentum from the scalar star. In the Proca case, by contrast, no instability is observed and the evolutions are compatible with the formation of a spinning Proca star. Secondly, we address the stability of an existing star, a stationary solution of the field equations. In the scalar case, a non-axisymmetric perturbation develops collapsing the star to a spinning black hole. No such instability is found in the Proca case, where the star survives large amplitude perturbations; moreover, some excited Proca stars decay to, and remain as, fundamental states. Our analysis suggests bosonic stars have different stability properties in the scalar/vector case, which we tentatively relate to their toroidal/spheroidal morphology. A parallelism with instabilities of spinning fluid stars is briefly discussed.