Relativistic and Newtonian Proca Stars: A Tale of Two Limits
Alberto Diez-Tejedor, Carlos Herdeiro, Claudio Lazarte, Eugen Radu, Armando A. Roque, Nicolas Sanchis-Gual, Etevaldo dos Santos Costa Filho
arxiv.org/abs/2606.13785 [ππ-ππ πππππ-ππ.π²πΎ πππ-ππ]
ALT We investigate a representative set of static solitonic solutions of the Einstein-Proca theory in the Newtonian regime, where the field frequency approaches the particle mass, Οβ ΞΌ, and compare them with the corresponding solutions of the spin-1 SchrΓΆdinger-Poisson system, which provides the effective description in this limit. While this correspondence is relatively straightforward in the Einstein-Klein-Gordon case, the vector nature of the Proca field, combined with the enhanced U(3) symmetry of the nonrelativistic spin-1 regime, gives rise to several nontrivial features that require careful analysis. We establish a mapping between the two descriptions by identifying β=0 electric Proca stars with radially polarized (hedgehog) configurations and β=1 electric Proca stars with linearly polarized configurations. We further clarify some aspects of the ground state and resolve several apparent discrepancies between relativistic and Newtonian solutions, particularly concerning their morphol