Complex Kerr Geometry, Twistors and the Dirac Electron

TL;DR

This paper explores the deep connection between the Dirac electron and Kerr-Newman geometry, showing how the Dirac equation integrates into Kerr-Schild formalism and influences the space-time structure of spinning particles.

Contribution

It demonstrates that the Dirac equation can be incorporated into Kerr geometry as a master equation, linking wave functions to twistorial structures and gravitational fields.

Findings

The Dirac wave function controls Kerr-Newman space-time polarization.

The Dirac equation naturally fits into Kerr-Schild formalism.

Wave functions act as order parameters for spin and dynamics.

Abstract

The Kerr-Newman spinning particle displays some remarkable relations to the Dirac electron and has a reach spinor structure which is based on a twistorial description of the Kerr congruence determined by the Kerr theorem. We consider the relation between this spinor-twistorial structure and spinors of the Dirac equation, and show that the Dirac equation may naturally be incorporated into Kerr-Schild formalism as a master equation controlling the twistorial structure of Kerr geometry. As a result, the Dirac electron acquires an extended space-time structure having clear coordinate description with natural incorporation of a gravitational field. The relation between the Dirac wave function and Kerr geometry is realized via a chain of links: {\it Dirac wave function $ \Rightarrow $ Complex Kerr-Newman Source $ \Rightarrow $ Kerr Theorem $ \Rightarrow $ Real Kerr geometry.} As a result, the wave function acquires the role of an ``order parameter'' which controls spin, dynamics, and twistorial polarization of Kerr-Newman space-time.