Complex Structure of the Four-Dimensional Kerr Geometry: Stringy System, Kerr Theorem, and Calabi-Yau Twofold

TL;DR

This paper explores the deep connections between four-dimensional Kerr geometry, string theory, and Calabi-Yau structures, revealing how complex and stringy features emerge naturally within the Kerr spacetime framework.

Contribution

It demonstrates the emergence of Calabi-Yau twofolds in Kerr geometry's twistorial structure and links Kerr stringy systems to complex embeddings of superstrings.

Findings

Calabi-Yau twofold (K3 surface) appears in Kerr geometry's twistorial structure.

Kerr singular ring's lightlike fields resemble heterotic string solutions.

Kerr stringy system may relate to complex N=2 superstring embedding.

Abstract

The 4d Kerr geometry displays many wonderful relations with quantum world and, in particular, with superstring theory. The lightlike structure of fields near the Kerr singular ring is similar to the structure of Sen solution for a closed heterotic string. Another string, open and complex, appears in the complex representation of the Kerr geometry initiated by Lind and Newman . Combination of these strings forms a membrane source of the Kerr geometry which is parallel to the string/M-theory unification. In this paper we give one more evidence of this relationship, emergence of the Calabi-Yau twofold (K3 surface) in twistorial structure of the Kerr geometry as a consequence of the Kerr theorem. Finally, we indicate that the Kerr stringy system may correspond to a complex embedding of the critical N=2 superstring.