Lightons and Helixons as Lightlike Particles in General Relativity

TL;DR

This paper explores how the gravitational fields of massive particles in General Relativity transition into those of lightlike particles, called lightons and helixons, through a limiting process affecting their algebraic classification.

Contribution

It introduces the concept of lightlike limits transforming Schwarzschild, Kerr, and NUT fields into lightlike particles, revealing phase transitions in Petrov's algebraic types.

Findings

Gravitational fields of massive particles become lightlike particles under the limit.

The transition involves a change from Petrov type D to N or III.

Lightlike sources in GR have no 'hairs'.

Abstract

The exterior gravitational fields of the massive Schwarzschild, Kerr and NUT particles have an algebraic type {\bfseries D} according to Petrov's algebraic classification of the gravitational fields. A lightlike limit is input for these particles. It is shown that under this limiting procedure the gravitational fields of the particles are transformed into the gravitational fields of the lightlike particles a lighton and a helixon. On the other hand this limit can be described as a cusp catastrophe on a level of Weyl's matrix with a change of a gravitational field symmetry of such sources. In considered cases we have a phase gravitational transition of second kind from {\bfseries D} type into {\bfseries N} type or {\bfseries III} type. There is a transition of one "phase" to another. Petrov's algebraic types are the different "phases" of the gravitational field. It is shown that the lightlike sources in General Relativity "have no hairs".