Asymptotically flat gravitating spinor field solutions. Step 2 - the compatibility of Dirac equations in a curve and a flat spaces

TL;DR

This paper investigates how to modify the spin connection in curved spacetime to ensure the Dirac equation remains compatible with its flat spacetime form, addressing a fundamental aspect of spinor fields in general relativity.

Contribution

It proposes a modification to the spin connection to achieve compatibility of Dirac equations in curved and flat spaces.

Findings

Modified spin connection ensures Dirac equation consistency

Provides a framework for spinor fields in curved spacetime

Addresses compatibility issues in general relativity

Abstract

Using the fact that a spin connection is defined to an accuracy of a vector it is shown that the spin connection should be modified in such a manner that Dirac equation in a curve space would be compatible with Dirac equation in a flat space.