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

In this paper we present a detailed calculation of an Ansatz that allows to obtain spherically symmetric Einstein–Dirac configurations in d-dimensions. We show that this is possible by combining $$2^{\lfloor \frac{d-2}{2} \rfloor }$$ Dirac fields, making use of the properties of the angular dependence of the spinors in a spherical background. By applying this Ansatz, we investigate some simple analytical solutions. One of them is a regular wormhole supported by the Dirac fields. Other solutions include a pathological black hole and a naked singularity. We analyze the domain of existence and properties of all these solutions.