Stringlike structures in the real and complex Kerr-Schild geometry

TL;DR

This paper explores the intricate relationship between Kerr-Schild geometry, superstring theory, and twistor space, revealing complex structures like Calabi-Yau manifolds and membranes that bridge gravity and quantum theories.

Contribution

It uncovers how Kerr-Schild geometry relates to superstring models, complex structures, and Calabi-Yau manifolds, providing a novel geometric framework linking gravity and string theory.

Findings

Kerr-Newman solution's gyromagnetic ratio matches Dirac electron

Kerr singular ring forms a point-string-membrane complex

Kerr theorem's null congruence creates a Calabi-Yau twofold in twistor space

Abstract

Four-dimensional Kerr-Schild (KS) geometry displays remarkable relationships with quantum world and theory of superstrings. In particular, the Kerr-Newman (KN) solution has gyromagnetic ratio g = 2, as that of the Dirac electron and represents a consistent background for gravitational and electromagnetic field of the electron. As a consequence of very big spin/mass ratio, black hole horizons disappear, exposing the naked Kerr singular ring. We consider four-decade history of development of this structure which took finally the form of a point-string-membrane-bubble complex which is reminiscent of the enhancon model of string/M-theory. A complex string obtained in the complex structure of the Kerr geometry gives an extra dimension to the world-sheet of the real Kerr string, forming a membrane by analogue with the string/M-theory unification. By analysis of the orientifold parity of the complex Kerr string, we obtain that the determined by the Kerr theorem principal null congruence of the Kerr geometry is described by a quartic equation in projective twistor space CP3, and therefore, it creates the known Calabi- Yau twofold (K3 surface) in twistor space of the 4d KS geometry. We connect it with N=2 superstring which has (complex) critical dimension two and may be embedded into complex KS geometry.