P.T. Chrusciel

Title: Polyhomogeneous Scri's

Abstract: In this talk I will review the evidence that generic asymptotically Minkowskian radiating space-times will have a conformal completion at null infinity which is polyhomogeneous rather than smooth. I will start by recalling the definition of polyhomogeneous functions. I will review the Bondi - van der Burgh - Metzner - Sachs analysis, pointing out that generic solutions of the characteristic constraint equations are polyhomogeneous in 1/r, where r is an area coordinate. I will review the results of the analysis by Lars Andersson, myself, and Helmut Friedrich, which show that solutions of the constraint equations on hyperboloidal hypersurfaces obtained from generic smooth seed fields are polyhomogeneous. Finally I will point out the results, obtained in collaboration with Olivier Lengard, on existence of Scri for solutions of the vacuum Einstein equations with polyhomogeneous hyperboloidal initial data. The references to my work on those problems are: A short description of the issues that arise here can also be found in paragraph 5 of the research section of my home page.

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Copyright 29.VIII.02 by P.T.Chrusciel and A.Chopin