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arXiv · 0710.4249

Complex Kerr Geometry, Twistors and the Dirac Electron

Alexander Burinskii
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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.

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Alexander Burinskii. 2008-03-11. Complex Kerr Geometry, Twistors and the Dirac Electron. https://doi.org/10.1088/1751-8113/41/16/164069

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