Complex structure of Kerr-Schild geometry: Calabi-Yau twofold from the Kerr theorem

TL;DR

This paper explores the complex structure of Kerr geometry, revealing a Calabi-Yau twofold derived from the Kerr theorem, linking four-dimensional gravity with superstring theory concepts.

Contribution

It demonstrates that Kerr geometry's twistorial structure naturally leads to a Calabi-Yau twofold, bridging classical gravity and superstring theory frameworks.

Findings

Kerr geometry can be represented as a complex string with independent endpoints.

The Kerr theorem yields a quartic in projective twistor space, identified as a Calabi-Yau twofold.

Kerr geometry is a four-dimensional theory compatible with gravity at the Compton scale.

Abstract

We consider Newman's representation of the Kerr geometry as a complex retarded-time construction generated by a source propagating along a complex world-line. We notice that the complex world-line forms really an open complex string, endpoints of which should have independent dynamics by the string excitations. The adjoined to complex Kerr string twistorial structure is determined by the Kerr theorem, and we obtain that the resulting Kerr's equation describes a quartic in projective twistor $CP^3 ,$ which is known as Calabi-Yau twofold of superstring theory. Along with other remarkable similarities with superstring theory, the Kerr geometry has principal distinctions being the four-dimensional theory consistent with gravity at the Compton scale, contrary to the Planck scale of the superstring theory.