Remarks on exact solutions

This paper first discusses the historical context of the influential “Exact Solutions” book, which was co-authored by Malcolm MacCallum. It then makes various technical points about such solutions. It is useful to characterize solutions in terms of the properties of matter they contain or the kinds of test particle motions which are possible. It is also interesting to consider which isometries are implied by particular kinds of matter behaviour. Judging the validity of an approximation by the smallness of the tensor components can be misleading. Finally, an example is given of a result which is obvious in Newtonian theory but little understood in General Relativity.