The Smoothness of Null Infinity: Its Relevance for Numerical Relativity

Details The Smoothness of Null Infinity: Its Relevance for Numerical Relativity The Smoothness of Null Infinity: Its Relevance for Numerical Relativity

Feb 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005tmgm.meet.1613v&link_type=abstract

The Tenth Marcel Grossmann Meeting. Proceedings of the MG10 Meeting held at Brazilian Center for Research in Physics (CBPF), Rio

Physics

Scientific paper

The conformal approach to the description of isolated systems in General Relativity based on the notion of asymptotic simplicity usually assumes that the conformal boundary --null infinity-- is a smooth submanifold. Some work on the so-called polyhomogeneous spacetimes has shown that much of the standard formalism holds on much weaker assumptions on the smoothness of null infinity. Furthermore, some recent work has shown that developments of Misner and Brill-Lindquist data have a non-smooth boundary. The latter raises the questions regarding the suitability of smooth null infinity to model "realistic" systems as different assumptions of the smoothness of the conformal boundary would yield slightly different physical predictions. This is an issue that is not only of relevance not for numerical simulations based on the conformal approach but in general for any code simulating asymptotically flat systems as some sort of asymptotic behaviour must at any rate be prescribed in order to model the "isolatedness" of the system. This prescribed asymptotic behaviour will contain implicit and explicit assumptions regarding the smoothness of null infinity. The relation between hyperboloidal initial data and Cauchy initial data is discussed within this context.

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