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

TL;DR

This paper develops an Ansatz to construct spherically symmetric Einstein-Dirac systems with multiple spinors in various dimensions, leading to analytical solutions including a wormhole, a black hole, and a naked singularity, and analyzes their properties.

Contribution

It introduces a novel Ansatz for spherically symmetric Einstein-Dirac configurations with multiple spinors in arbitrary dimensions, enabling analytical solution construction.

Findings

A regular wormhole supported by Dirac fields is found.

Solutions include a black hole and a naked singularity.

The domain of existence and properties of these solutions are analyzed.

Abstract

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.