Twistor String Structure of the Kerr-Schild Geometry and Consistency of the Dirac-Kerr System
Abstract
Kerr-Schild (KS) geometry of the rotating black-holes and spinning particles is based on the associated with Kerr theorem twistor structure which is defined by an analytic curve F(Z)=0 in the projective twistor space Z ∈ CP3 . On the other hand, there is a complex Newman representation which describes the source of Kerr-Newman solution as a "particle" propagating along a complex world-line X()∈ CM4, and this world-line determines the parameters of the Kerr generating function F(Z). The complex world line is really a world-sheet, = t + i σ, and the Kerr source may be considered as a complex Euclidean string extended in the imaginary time direction σ. The Kerr twistor structure turns out to be adjoined to the Kerr complex string source, forming a natural twistor-string construction similar to the Nair-Witten twistor-string. We show that twistor polarization of the Kerr-Newman solution may be matched with the massless solutions of the Dirac equation, providing consistency of the Dirac-Kerr model of spinning particle (electron). It allows us to extend the Nair-Witten concept on the scattering of the gauge amplitudes in twistor space to include massive KS particles.