The techniques used by Andersson and Moncrief are similar to those used by Christodoulou and Klainerman. In particular, the Bel-Robinson tensor is crucial. However their situation is much simpler than that of Christodoulou and Klainerman, so that the complexity of the proof is not so great. This has to do with the fact that the fall-off of the fields in the Minkowksi case towards infinity is different in different directions, while it is uniform in the Milne case. Thus it is enough in the latter case to always contract the Bel-Robinson tensor with the same timelike vector when deriving energy estimates. The fact that the proof is simpler opens up a real possibility of generalizations, for instance by adding different matter models.
|Local and Global Existence Theorems for the Einstein
Alan D. Rendall
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