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Kerr-Schild (KS) geometry of the rotating black-holes and spinning particlesis based on the associated with Kerr theorem twistor structure which is definedby an analytic curve $F(Z)=0$ in the projective twistor space $Z \in CP^3 .$ Onthe other hand, there is a complex Newman representation which describes thesource of Kerr-Newman solution as a "particle" propagating along a complexworld-line $X(\t)\in CM^4,$ and this world-line determines the parameters ofthe Kerr generating function $F(Z).$ The complex world line is really aworld-sheet, $\t= t + i \sigma,$ and the Kerr source may be considered as acomplex Euclidean string extended in the imaginary time direction $\sigma$. TheKerr twistor structure turns out to be adjoined to the Kerr complex stringsource, forming a natural twistor-string construction similar to theNair-Witten twistor-string. We show that twistor polarization of theKerr-Newman solution may be matched with the {\it massless} solutions of theDirac equation, providing consistency of the Dirac-Kerr model of spinningparticle (electron). It allows us to extend the Nair-Witten concept on thescattering of the gauge amplitudes in twistor space to include massive KSparticles.

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