a New Class of Obstructions to the Smoothness of Null Infinity

Details a New Class of Obstructions to the Smoothness of Null Infinity a New Class of Obstructions to the Smoothness of Null Infinity

Feb 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005tmgm.meet.1838k&link_type=abstract

THE TENTH MARCEL GROSSMANN MEETING PART A On Recent Developments in Theoretical and Experimental General Relativity, Gravitation

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Scientific paper

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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