Gravitational fields of lightons and helixons in General Relativity

Abstract

A lightlike limit procedure for massive particles of Schwarzschild, Kerr and NUT which are sources of the exterior gravitational fields of an algebraic type D is introduced. It is shown when a velocity of fast moving massive particles along z axis tends towards the light velocity axis and the total energy of each particle is constant (i.e. a rest mass of the particle tends towards zero) together with Kerr's angular momentum along z axis and with NUT's parameter which also tend to constants then the gravitational fields of these fast moving particles tend towards the wave's fields of the N and III algebraic types as their limits. The lightlike limit of massive particle may be described as cusp catastrophe on the level of Weyl's matrix with a change of gravitational field's symmetry of such source. In considered cases such limit is a phase transition of the gravitational field from D type into N type or III type (transition from one "phase" to another). Petrov's algebraic types are different "phases" of gravitational field. As result of the lightlike limit procedure the lightlike scalar massless particle ({\it lighton}) and a vector lightlike massless particle with a helicity ({\it helixon}) are obtained. It is shown the lightlike sources in General Relativity "have no hairs"