κ -Dirac stars

In this paper, we construct a Dirac star model composed of |κ | pairs of spinor fields. The azimuthal harmonic indices m of these spinor fields are half-integers, and they satisfy -(|κ |-1/2)≤ m ≤ |κ |-1/2 . When κ =1 , it corresponds to the conventional Dirac star model, formed by two spinor fields with m=1/2 and m=-1/2 . When |κ |>1 , among these |κ | pairs of spinor fields, there exist spinor fields with azimuthal harmonic indices m>1/2 , and all spinor fields still conform to the same Dirac field equation. Different families of solutions are distinguished by the value of κ , so we named these solutions κ -Dirac stars. We obtain solutions for κ =± 1,± 2,± 3,± 4,± 5,± 6 by using numerical methods. Additionally, we compute their ADM mass M, Noether charge Q, and binding energy E, and illustrate how these quantities change with the spinor field’s frequency ω for different κ . We observe significant differences between solutions for |κ |>1 and the |κ |=1 case. Furthermore, we provide the energy density distribution of the Dirac stars, wherein for |κ |>1 scenarios, the Dirac stars exhibit a spherical shell-like structure. Moreover, we employ three-dimensional diagrams to intuitively depict how κ influences the combination of spinor fields to form a spherically symmetric configuration.