Wonderful Consequences of the Kerr Theorem

TL;DR

This paper extends Kerr's multi-particle solution using the Kerr theorem, revealing a multi-sheeted twistorial spacetime with unique internal structures and interactions via singular twistor lines, suggesting a link to quantum gravity.

Contribution

It introduces a multi-particle Kerr-Newman solution with a novel twistorial structure and internal spaces, providing a geometric framework potentially relevant to quantum gravity.

Findings

Multi-sheeted, multi-twistorial spacetime with internal particle spaces.

Interactions occur via singular twistor lines connecting particles.

The structure suggests a link to stringy vacuum structures and quantum gravity.

Abstract

Kerr's multi-particle solution is obtained on the base of the Kerr theorem. Choosing generating function of the Kerr theorem $F$ as a product of partial functions $F_i$ for spinning particles i=1,...k, we obtain a multi-sheeted, multi-twistorial space-time over $M^4$ possessing unusual properties. Twistorial structures of the i-th and j-th particles do not feel each other, forming a type of its internal space. Gravitation and electromagnetic interaction of the particles occurs via a singular twistor line which is common for twistorial structures of interacting particles. The obtained multi-particle Kerr-Newman solution turns out to be `dressed' by singular twistor lines linked to surrounding particles. We conjecture that this structure of space-time has the relation to a stringy structure of vacuum and opens a geometrical way to quantum gravity.