Massless Fermions in planar Bianchi type I universes: Exact and approximate solutions

TL;DR

This paper derives exact and approximate solutions for massless fermions in anisotropic Bianchi type I universes, revealing how solutions can be generated and characterized by parameters, with applications to Kasner backgrounds.

Contribution

It introduces a method to generate all solutions within an equivalence class of Bianchi I models from a single known solution, including approximate solutions with correct asymptotic behavior.

Findings

Solutions form equivalence classes characterized by two parameters.

All solutions in a class can be generated from one known solution.

Approximate solutions accurately describe early and late-time behavior.

Abstract

Based upon the exact formal solutions of the Weyl-Dirac-equation in anisotropic planar Bianchi-type-I background spacetimes with power law scale factors, one can introduce suitable equivalence classes of the solutions of these models. The associated background spacetimes are characterized by two parameters. It is shown that the exact solutions of all models of a given equivalence class can be generated with the help of a special transformation of these two parameters, provided one knows a single exact solution of an arbitrary member of this class. The method can also be utilized to derive approximate solutions, i.e. solutions which exhibit the correct behavior at early and at late times as well. This is explicitly demonstrated for the case of the anisotropic Kasner background with axial symmetry.