Asymptotically flat gravitating spinor field solutions. Step 3 - Einstein-Dirac equations: cylindric case

TL;DR

This paper derives self-consistent Einstein-Dirac equations for two gravitating spinor fields using specific ansätze to simplify the energy-momentum tensor, advancing understanding of spinor solutions in curved spacetime.

Contribution

It introduces a method to obtain self-consistent Einstein-Dirac equations for two spinor fields with specific ansätze to simplify the tensor components.

Findings

Derived self-consistent Einstein-Dirac equations for two spinor fields.

Demonstrated how to use ansätze to zero off-diagonal energy-momentum tensor components.

Provided a framework for analyzing gravitating spinor solutions in cylindric spacetime.

Abstract

Einstein-Dirac equations for two spinor fields are considered. It is shown that in this case one can obtain self-consistent equations set for these gravitating spinors. The key idea to obtain Einstein-Dirac equations is to use special ans\"atze for spinor fields in order to zero some off-diagonal componentes of the spinor energy - momentum tensor.