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Smoothness at null infinity and the structure of initial data. (English) Zbl 1072.83003
Chruściel, Piotr T. (ed.) et al., The Einstein equations and the large scale behavior of gravitational fields. 50 Years of the Cauchy problem in general relativity. With DVD. Basel: Birkhäuser (ISBN 3-7643-7130-7/hbk). 121-203 (2004).
The article gives an overview about the present research on the relation between the behavior of asymptotically flat Cauchy data for Einstein’s vacuum equations near space-like infinity and the asymptotic behavior of their evolution in time at null infinity. This consideration is of great importance for the understanding of the gravitational radiation of isolated self-gravitating systems.
In order to analyse the behavior of the gravitational field near space-like and null infinity according to Einstein’s vacuum field equation a conformal representation (general conformal field equations) of this equation is introduced. It is assumed that the spacetime has the property of asymptotic simplicity to guarantee that the fall-off behavior can be characterized geometrically. The choice of the asymptotically flat Cauchy data is described and considered in detail for static initial data. The construction of the regular finite initial value problem at space-like infinity is discussed. Recent results for conformal extensions of static vacuum space-times are given.
The rich list of references enables the reader to follow the several special topics in detail.
For the entire collection see [Zbl 1048.83001].

MSC:
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83C30 Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory
83C35 Gravitational waves
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