$$\kappa $$ κ -Dirac stars

Abstract

Abstract In this paper, we construct a Dirac star model composed of $$|\kappa |$$ | κ | pairs of spinor fields. The azimuthal harmonic indices m of these spinor fields are half-integers, and they satisfy $$-(|\kappa |-\frac{1}{2})\le m \le |\kappa |-\frac{1}{2}$$ - ( | κ | - 1 2 ) ≤ m ≤ | κ | - 1 2 . When $$\kappa =1$$ κ = 1 , it corresponds to the conventional Dirac star model, formed by two spinor fields with $$m=\frac{1}{2}$$ m = 1 2 and $$m=-\frac{1}{2}$$ m = - 1 2 . When $$|\kappa |>1$$ | κ | > 1 , among these $$|\kappa |$$ | κ | pairs of spinor fields, there exist spinor fields with azimuthal harmonic indices $$m>\frac{1}{2}$$ 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 $$\kappa $$ κ , so we named these solutions $$\kappa $$ κ -Dirac stars. We obtain solutions for $$\kappa =\pm 1,\pm 2,\pm 3,\pm 4,\pm 5,\pm 6$$ 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 $$\omega $$ ω for different $$\kappa $$ κ . We observe significant differences between solutions for $$|\kappa |>1$$ | κ | > 1 and the $$|\kappa |=1$$ | κ | = 1 case. Furthermore, we provide the energy density distribution of the Dirac stars, wherein for $$|\kappa |>1$$ | κ | > 1 scenarios, the Dirac stars exhibit a spherical shell-like structure. Moreover, we employ three-dimensional diagrams to intuitively depict how $$\kappa $$ κ influences the combination of spinor fields to form a spherically symmetric configuration.