Multi-state Dirac stars

In this paper, we construct the multi-state Dirac stars (MSDSs) consisting of two pairs of Dirac fields. The two pairs of Dirac fields are in the ground state and the first excited state, respectively, with opposite spins to ensure that the system possesses spherical symmetry. We discuss the solutions of the MSDSs under synchronized and nonsynchronized frequencies. By varying the ratio of masses between the two sets of Dirac fields, different branches of solutions can be obtained. Furthermore, we analyze the characteristics of the various MSDSs solutions and analyze the relationship between the ADM mass M of the MSDSs and the synchronized and nonsynchronized frequencies. Subsequently, we calculate the binding energy E_B of the MSDSs and discuss the stability of the solutions. Then, we investigated the solutions of the MSDSs under the single particle condition. Finally, we discuss the feasibility of simulating the dark matter halos using MSDSs.