The Kerr theorem and multiparticle Kerr-Schild solutions

TL;DR

This paper extends the Kerr theorem to construct exact multiparticle Einstein-Maxwell solutions with multi-sheeted twistorial structures, revealing particles connected by light-like twistor lines, potentially linking classical solutions to quantum theory.

Contribution

It introduces an extended Kerr theorem for multiparticle solutions with multi-sheeted structures and twistor-based interactions, offering new insights into classical and quantum gravity connections.

Findings

Multiparticle Kerr-Schild solutions with multi-sheeted twistorial structures.

Particles connected via light-like singular twistor lines.

Potential implications for quantum theory and quantum gravity.

Abstract

We discuss and prove an extended version of the Kerr theorem which allows one to construct exact solutions of the Einstein-Maxwell field equations from a holomorphic generating function $F$ of twistor variables. The exact multiparticle Kerr-Schild solutions are obtained from generating function of the form $F=\prod_i^k F_i, $ where $F_i$ are partial generating functions for the spinning particles $ i=1...k$. Solutions have an unusual multi-sheeted structure. Twistorial structures of the i-th and j-th particles do not feel each other, forming a type of its internal space. Gravitational and electromagnetic interaction of the particles occurs via the light-like singular twistor lines. As a result, each particle turns out to be `dressed' by singular pp-strings connecting it to other particles. We argue that this solution may have a relation to quantum theory and to quantum gravity.