Boson and Dirac stars in D ≥ 4 dimensions

Abstract

We present a comparative study of spherically symmetric, localized, particle-like solutions for spin s = 0, 1/2 and 1 gravitating fields in a D-dimensional, asymptotically flat spacetime. These fields are massive, possessing a harmonic time dependence and no self-interaction. Special attention is paid to the mathematical similarities and physical differences between the bosonic and fermonic cases. We find that the generic pattern of solutions is similar for any value of the spin s, depending only on the dimensionality of spacetime, the cases D = 4, 5 being special.

Perturbing the ground state of Dirac stars

“…where n is the separation constant and ð (s) (25) We thus find that Θ 1 = +1/2 Y m and Θ 2 = −1/2 Y m are spin-weighted spherical harmonics. We will find below that having only one spin-1/2 fermion violates spherical symmetry and that to preserve spherical symmetry we need two (or more) fermions.…”

“…Our study is entirely classical, just as with [23,27,28]. It remains to be determined how important quantum effects are to Dirac stars [18,25]. We only considered Dirac stars in the ground state.…”

“…Dynamical solutions of the Einstein-Dirac system [23,24] were initiated by Ventrella and Choptuik [23] in a study of type II critical collapse. More recently a comparison of the space of static solutions for boson, Dirac, and Proca stars was given in [18,25], Dirac star solutions in which the fermions have interactions were found in [26][27][28], and for the first time spinning Dirac stars were solved for in [29].…”

Constructing spherically symmetric Einstein–Dirac systems with multiple spinors: Ansatz, wormholes and other analytical solutions

“…The next equation (18) tells us that the matrix governing the projection onto the (n − 2)-sphere commutes with the matrices of the (n − 2)-sphere. The last equation (19) shows that the projected γ-matrices on the (n− 2)-sphere commute with the γ-matrices on the sliced off two-sphere.…”

“…The properties of such multi-Dirac soliton-like solutions have been recently studied in [19], where their properties were compared with similar configurations made of scalar and Proca fields for d ≥ 4. It was shown that some generic features of the solutions actually do not depend qualitatively on the spin of the field, but they are controlled by the dimension of the space-time.…”