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

TL;DR

This paper explores the twistor string structure underlying Kerr-Schild geometry of rotating black holes and particles, linking it with the Dirac equation to support a consistent model of spinning particles like the electron.

Contribution

It introduces a twistor-string framework for Kerr-Schild geometry and demonstrates its compatibility with Dirac solutions, extending twistor amplitude concepts to massive particles.

Findings

Kerr twistor structure is linked to a complex string source.

Matching twistor polarization with massless Dirac solutions.

Supports a consistent Dirac-Kerr model for spinning particles.

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 $Z \in CP^3 .$ 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.