3.6 Going further

Readers who are interested in obtaining information about the current status of existence theorems in general relativity are referred to Rendall’s Living Reviews article [137].

Although we have restricted ourselves to the case of a vanishing cosmological constant this does not mean that other cases have not been analyzed. Friedrich [62Jump To The Next Citation Point] has shown the existence of asymptotically simple de Sitter type solutions of the Einstein-Maxwell–Yang–Mills equations and stability of de Sitter space. More recently [64], with the general version of his conformal field equations, he was able to demonstrate the existence of asymptotically simple anti-de Sitter type solutions.

It should also be mentioned that some work has gone into generalizing the Bondi–Sachs calculations to poly-homogeneous space-times [34160161].

The structure of space-like infinity has been discussed here only in a rather cursory way. A very recent account of the relationship between static solutions and the role they play can be found in [70]. Readers who are interested in a more detailed treatment of the subject in general are referred to a recent review by Friedrich [68].


  Go to previous page Go up Go to next page