Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-11-07
Commun.Math.Phys. 244 (2004) 133-156
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
24 pages, 4 figures
Scientific paper
10.1007/s00220-003-0967-5
Expansions of the gravitational field arising from the development of asymptotically Euclidean, time symmetric, conformally flat initial data are calculated in a neighbourhood of spatial and null infinities up to order 6. To this ends a certain representation of spatial infinity as a cylinder is used. This set up is based on the properties of conformal geodesics. It is found that these expansions suggest that null infinity has to be non-smooth unless the Newman-Penrose constants of the spacetime, and some other higher order quantities of the spacetime vanish. As a consequence of these results it is conjectured that similar conditions occur if one were to take the expansions to even higher orders. Furthermore, the smoothness conditions obtained suggest that if a time symmetric initial data which is conformally flat in a neighbourhood of spatial infinity yields a smooth null infinity, then the initial data must in fact be Schwarzschildean around spatial infinity.
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