Twistor String Structure of the Kerr-Schild Geometry and Consistency of the Dirac-Kerr System

Details Twistor String Structure of the Kerr-Schild Geometry and Consistency of the Dirac-Kerr System Twistor String Structure of the Kerr-Schild Geometry and Consistency of the Dirac-Kerr System

2008-12-29

arxiv.org/abs/0812.4908v1

THE PROBLEMS OF MODERN COSMOLOGY. A volume in honour of Professor S.D. Odintsov in the occasion of his 50 th birthday. pp.129-

Physics

High Energy Physics

High Energy Physics - Theory

11 p. 2 figs. Dedicated to Jubilee of Prof. S.D.Odintsov, based on the talk at the 5th Math. Phys. Meeting, July 2008, Belgrad

Scientific paper

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 $Z \in CP^3 .$ 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 $X(\t)\in CM^4,$ and this world-line determines the parameters of the Kerr generating function $F(Z).$ The complex world line is really a world-sheet, $\t= t + i \sigma,$ and the Kerr source may be considered as a complex Euclidean string extended in the imaginary time direction $\sigma$. 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 {\it 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.

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