The Kerr theorem and multiparticle Kerr-Schild solutions

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 $i=\mathrm{1...}k$. 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.

13 pages, 4 figures, revtex. Expressions for electromagnetic field are corrected

References in corpus (1)

• Twistorial Analyticity and Three Stringy Systems of the Kerr Spinning Particle

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• Stringlike structures in the real and complex Kerr-Schild geometry
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• Complex Kerr Geometry, Twistors and the Dirac Electron