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Conformal scattering and the Goursat problem, main ideas and what perspectives for black hole space-times?

Tuesday 6th September 2005 - 15:30 to 16:30
INI Seminar Room 1

The general idea of conformal scattering theory is to replace the use of spectral techniques in the construction of a scattering theory by a geometric approach based on conformal compactification. The existence of a scattering operator is then interpreted as the well-posedness of the Goursat problem on null infinity. The advantage is that stationarity is no longer required for such constructions. When spacetimes contain energy, spacelike infinity is a singuarity of the conformal metric (the metric being not much better than Lipschitz there) and this requires techniques that allow us to deal with the Goursat problem in weak regularity.

We describe the essential ideas of the conformal scattering approach and their origin, and give the first results obtained in the framework of asymptotically simple spacetimes (from a joint work with Lionel Mason). For the resolution of the Goursat problem, we use a technique proposed by Lars Hormander for smooth metrics and extend it to metrics whose regularity is intermediate between ${\cal C}^1$ and Lipschitz (recent submitted work).

Then we turn to black hole space-times and describe the obstructions to such constructions in this case. These entail perspectives of further studies of the geometry of black hole space-times.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons