# Dirac star in the presence of Maxwell and Proca fields

## TL;DR

This paper investigates charged Dirac star configurations with nonlinear spinor fields coupled to Maxwell and Proca fields, demonstrating potential astrophysical relevance and mass growth with charge and coupling constants through numerical analysis.

## Contribution

It introduces a new model of Dirac stars with nonlinear spinor fields coupled to electromagnetic fields, analyzing their properties and mass behavior.

## Key findings

- Mass increases with charge and coupling constants.
- Configurations can have masses comparable to Chandrasekhar mass.
- Numerical results suggest possible astrophysical relevance.

## Abstract

We consider configurations consisting of a gravitating nonlinear spinor field $\psi$, with a nonlinearity of the type $\lambda\left(\bar\psi\psi\right)^2$, minimally coupled to Maxwell and Proca fields through the coupling constants $Q_M$ [U(1) electric charge] and $Q_P$, respectively. In order to ensure spherical symmetry of the configurations, we use two spin-$1/2$ fields having opposite spins. By means of numerical computations, we find families of equilibrium configurations with a positive Arnowitt-Deser-Misner (ADM) mass described by regular zero-node asymptotically flat solutions for static Maxwell and Proca fields and for stationary spinor fields. For the case of the Maxwell field, it is shown that, with increasing charge $Q_M$, the masses of the objects increase and diverge as the charge tends to a critical value. For negative values of the coupling constant $\lambda$, we demonstrate that, by choosing physically reasonable values of this constant, it is possible to obtain configurations with masses comparable to the Chandrasekhar mass and with effective radii of the order of kilometers. It enables us to speak of an astrophysical interpretation of such systems, regarding them as charged Dirac stars. In turn, for the system with the Proca field, it is shown that the mass of the configurations also grows with increasing both $|\lambda|$ and the coupling constant $Q_P$. Although in this case the numerical calculations do not allow us to make a definite conclusion about the possibility of obtaining masses comparable to the Chandrasekhar mass for physically reasonable values of $\lambda$, one may expect that such masses can be obtained for certain values of free parameters of the system under consideration.