After Einstein first presented his theory of general relativity in 1915, a few exact solutions of his field equations were found very quickly. All of these assumed a high degree of symmetry. Some could be interpreted as representing physically significant situations such as the exterior field of a spherical star, or a homogeneous and isotropic universe, or plane or cylindrical gravitational waves. Yet it took a long time before some of the more subtle properties of these solutions were widely understood.

In their seminal review of “exact solutions of the gravitational field equations”, Ehlers and Kundt (1962) included the following statement. “At present the main problem concerning solutions, in our opinion, is not to construct more but rather to understand more completely the known solutions with respect to their local geometry, symmetries, singularities, sources, extensions, completeness, topology, and stability.” Since this was written, considerable progress has been made in the understanding of many exact solutions. However, this development has been very restricted compared to the enormous effort that has been put into the derivation of further “new” solutions. Although significant advance has been achieved in the interpretation of many solutions, it is a fact that some aspects of even the most frequently quoted exact solutions still remain poorly understood. The opinion of Ehlers and Kundt thus still indicates an even more urgent task.

In this work, the very traditional approach will be adopted that an exact solution of Einstein's equations is expressed in terms of a metric in particular coordinates. Specifically, it will be represented in the form of a 3+1-dimensional line element in which the coordinates have certain ranges.