THE KERR THEOREM AND MULTI-PARTICLE KERR–SCHILD SOLUTIONS

Abstract

We discuss an extended version of the Kerr theorem which allows one to construct the exact solutions of the Einstein–Maxwell field equations from a holomorphic generating function F of twistor variables. The exact multi-particle Kerr–Schild solutions are obtained from generating function of the form [Formula: see text], where Fi are partial generating functions for the spinning particles i = 1 ⋯ k. Solutions have an unusual multi-sheeted structure. Twistorial structures of the ith and jth 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.