2003/11/05 by Vladimir V. Kassandrov
Physics and Astronomy · Mathematics · #math-ph #math.MP
published as Grav.Cosmol. 8 (2002) 57-62 · 6 pages, no figures. Proceedings of the V Asian-Pasific Conference on the Gravitation and Astrophysics, Moscow, September 2001
arxiv created 2003/11/05 · arxiv updated 2009/12/01
We explicitly demonstrate the existence of twistor and ambitwistor structure for the 4-dimensional complexified eikonal equation (CEE) and present its general solution consisting of two different classes. For both, every solution can be obtained from a generating twistor function in a purely algebraic way, via the procedure similar to that used in the Kerr theorem for shear-free null congruences. Bounded singularities of eikonal or of its gradient define some particle-like objects with nontrivial characteristics and dynamics. Example of a new static solution to CEE with a ring-like singularity is presented, and general principles of algebraic field theory - algebrodynamics - closely related to CEE are briefly discussed.