We construct and explore the physical properties of scalaroca stars: spherically symmetric solitonic solutions made of a complex scalar field $\mathrm{\Phi }$ and a complex Proca field $A^{\mu }$. We restrict our attention to configurations in which both fields are in the fundamental state and possess an equal mass, focusing on the cases when (i) the scalar and Proca fields are (nonlinearly) superimposed and do not interact with each other; and (ii) the scalar and Proca fields interact through the term $\alpha |\mathrm{\Phi }{|}^2{A}^{\mu }{A}_{\mu }$. The solutions are found numerically for the noninteracting case ($\alpha =0$) as well as for both signs of the interaction coupling constant $\alpha$. While pure (i.e., single–field) Proca/scalar boson stars are the most/least massive for weakly interacting fields, one can obtain more massive solutions for a sufficiently strong interaction. Besides, in the latter case, solutions can be either in a synchronized state—in which both fields have the same frequency—or in a nonsynchronized state. In addition, we observe that the coupling between the two fields allows solitonic solutions with a real scalar field. We further comment on the possibility of spontaneous scalarization and vectorization of the interacting solitonic solution.

• Received 6 May 2023
• Accepted 31 July 2023

DOI:https://doi.org/10.1103/PhysRevD.108.044044