Stringlike structures in Kerr-Schild geometry: N=2 string, twistors and Calabi-Yau twofold

TL;DR

This paper explores the string-like structures within Kerr-Schild geometry, revealing connections to twistors, Calabi-Yau twofolds, and complex embeddings that deepen understanding of Kerr-Newman solutions and their twistor space representations.

Contribution

It details the embedding of a Calabi-Yau twofold in Kerr geometry and links Kerr congruences to twistorial K3 surfaces, advancing geometric and string-theoretic insights.

Findings

Identification of two stringy structures in Kerr-Schild geometry.

Embedding of Calabi-Yau twofold (K3 surface) in Kerr geometry.

Connection between Kerr congruence and twistorial K3 surface.

Abstract

Four-dimensional Kerr-Schild geometry contains two stringy structures. The first one is the closed string formed by the Kerr singular ring, and the second one is an open complex string with was obtained in the complex structure of the Kerr-Schild geometry. The real and complex Kerr strings form together a membrane source of the over-rotating Kerr-Newman solution without horizon, $a =J/m >> m .$ It has also been obtained recently that the principal null congruence of the Kerr geometry, induced by the complex Kerr string, is determined by the Kerr theorem as a quartic in the projective twistor space, which corresponds to embedding of the Calabi-Yau twofold in the bulk of the Kerr geometry. In this paper we describe this embedding in details and show that the four folds of the twistorial K3 surface represent an analytic extension of the Kerr congruence created by antipodal involution.