Resolving the pathologies of self-interacting Proca fields: A case study of Proca stars

It has been argued that a self-interacting massive vector field is pathological due to dynamical formation of singular effective metric the field, which onset gradient or ghost instability. We discuss this singularity not necessarily fundamental problem but breakdown theory (EFT) description field. By using model ultraviolet (UV) completion we demonstrate Proca star, self-gravitating condensate continues exist even after EFT suffers from instability without any pathology at UV, in still valid and may be interpreted as standard high-density boson star UV perspective. On other hand, find broken before appears. This suggests heavy degree freedom spontaneously excited cure dynamically tends approach