Wonderful consequences of the Kerr theorem: multiparticle Kerr-Schild solutions. (English) Zbl 1180.83015

Summary: Kerr’s multiparticle solution is obtained on the basis of the Kerr theorem. Choosing the generating function \(F\) of the Kerr theorem as a product of partial functions \(F_i\) for spinning particles \(i=1,\dots,k\), we obtain a many-sheeted, multi-twistorial space-time over \(M^4\) possessing unusual properties. 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 a singular twistor line which is common for twistorial structures of interacting particles. The obtained multi-particle Kerr-Newman solution turns out to be ‘dressed’ by singular twistor lines linked with surrounding particles. We conjecture that this structure of space-time has a relation to the stringy structure of vacuum and opens a geometric way to quantum gravity.


83C15 Exact solutions to problems in general relativity and gravitational theory
83C57 Black holes