Complex Kerr Geometry, Twistors and the Dirac Electron

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.

12 pages, 3 figs. Talk at the conference QFEXT'07

References in corpus (13)

• Perturbative Gauge Theory As A String Theory In Twistor Space
• Regular Sources of the Kerr-Schild class for Rotating and Nonrotating Black Hole Solutions
• SOME PROPERTIES OF THE KERR SOLUTION TO LOW ENERGY STRING THEORY
• Complex Kerr Geometry and Nonstationary Kerr Solutions
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• Kerr-Newman solution as a Dirac particle
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• Rotating Black Hole, Twistor-String and Spinning Particle

Cited by in corpus (4)

• Nonsingular Dirac particles in spacetime with torsion
• Aligned electromagnetic excitations of a black hole and their impact on its quantum horizon
• Two-vortex structure of electron, nonlocality and Dirac equation
• Electromagnetic Fields in Kerr-Shild Space-Times