A Burinskii 2008 J. Phys. A: Math. Theor. 41 164069 doi:10.1088/1751-8113/41/16/164069
Complex Kerr geometry, twistors and the Dirac electron
A Burinskii
Show affiliationsThe Kerr 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 spacetime structure having a 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: Dirac wave function 
Complex Kerr Source Kerr Theorem 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 spacetime.
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Issue 16 (25 April 2008)
Received 23 October 2007, in final form 29 December 2007
Published 9 April 2008
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Complex Kerr geometry, twistors and the Dirac electron
A Burinskii 2008 J. Phys. A: Math. Theor. 41 164069
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