The possible motion of particles with negative mass was considered in the context of general relativity by Bondi (1957a). He found that exact solutions exist in which the interaction between two particles, one with positive and the other with negative mass, is such that they are both induced to accelerate in the same direction. He showed that such solutions could be described in terms of a metric that has boost and rotation symmetries, and that this includes “static” regions that can be described by the Weyl metric. The explicit solution representing such a situation was subsequently found by Bonnor and Swaminarayan (1964), who also obtained a number of related solutions of a similar kind, some of which contain particles with positive mass only, although conical singularities then exist on parts of the axis of symmetry. Further solutions of this type were subsequently found by Bičák, Hoenselaers and Schmidt (1983a,b). It is the purpose of this chapter to review such solutions.

Boost-rotation symmetric space-times

The general metric with boost and rotation symmetries can be expressed in the form (14.44) which was presented in the previous chapter. This describes the fields of uniformly accelerating and possibly rotating sources. Solutions of algebraic type D, for which the sources are black holes, have been described in Chapter 14 and will be considered further in Chapter 16. However, alternative accelerating and rotating sources are also possible, and some properties of such algebraically general space-times have been described by Pravdová and Pravda (2002) and in references cited therein.