Exact solutions for Weyl fermions with gravity

TL;DR

This paper derives all exact solutions for Weyl fermions interacting with gravity, revealing a PP-wave spacetime metric and a flag-dipole spinor field, advancing understanding of fermion-gravity interactions.

Contribution

It provides the first complete set of exact solutions for Weyl fermions coupled with gravity in a Weyl-Lewis-Papapetrou spacetime.

Findings

The metric is a PP-wave spacetime.

The spinor field is a flag-dipole.

All solutions are explicitly characterized.

Abstract

We consider the single-handed spinor field in interaction with its own gravitational field described by the set of field equations given by Weyl field equations written in terms of derivatives that are covariant with respect to the gravitational connection plus Einstein field equations soured with the energy tensor of the spinor: for the Weyl spinor and the ensuing spacetime of Weyl-Lewis-Papapetrou structure, we will find all exact solutions. The obtained solution for the metric tensor is that of a PP-wave spacetime while the spinor field is a flag-dipole.