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The Kerr theorem, Kerr-Schild formalizm and multiparticle Kerr-Schild solutions

Alexander Burinskii
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Abstract

We consider an extended version of the Kerr theorem incorporated in the Kerr-Schild formalism. It allows one to construct the series of 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$. Gravitational and electromagnetic interaction of the spinning particles occurs via the light-like singular twistor lines. As a result, each spinning particle turns out to be `dressed' by singular pp-strings connecting it to other particles. Physical interpretation of this solution is discussed.

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Alexander Burinskii. 2006-10-02. The Kerr theorem, Kerr-Schild formalizm and multiparticle Kerr-Schild solutions. https://arxiv.org/abs/gr-qc/0610007

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