Constructing spherically symmetric Einstein–Dirac systems with multiple spinors: Ansatz, wormholes and other analytical solutions
José Luis Blázquez-Salcedo, Christian Knoll
Abstract
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 $$2^{\lfloor \frac{d-2}{2} \rfloor }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mo>⌊</mml:mo><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:mfrac><mml:mo>⌋</mml:mo></mml:mrow></mml:msup></mml:math> 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.