zbMATH — the first resource for mathematics

Time asymmetric spacetimes near null and spatial infinity. I: Expansions of developments of conformally flat data. (English) Zbl 1073.83015
The author of this interesting paper studies the behavior of the gravitational field near null and spatial infinity for the development of data, which are asymptotically Euclidean, conformally flat and time asymmetric. The spatial infinity is represented as a cylinder introduced by Friedrich. The conformal Einstein equations imply a hierarchy of transport equations. This serves to calculate asymptotic expansions for the gravitational field in a recursive way. It is found that the solutions of these transport equations have logarithmic divergences at the critical sets where null infinity meets spatial infinity. It is shown that there is a series of quantities expressible in terms of the initial data (so called obstructions). These obstructions are, in general, time asymmetric. Here a result of interest is that if the sets of obstructions vanish up to a certain order, then the initial data will be asymptotically Schwarzschildean in a certain sense.

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C30 Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory
Full Text: DOI