The Kerr theorem and multiparticle Kerr-Schild solutions

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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=∏ᵢᵏ Fᵢ, where Fᵢ 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.