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SUMMARY:Interaction of impulsive gravitational waves and related low-regul
 arity  problems in General Relativity - Maxime Van de Moortel
DTSTART:20181121T160000Z
DTEND:20181121T170000Z
UID:TALK113917@talks.cam.ac.uk
CONTACT:65944
DESCRIPTION:In General Relativity\, an impulsive gravitational wave is an 
 idealisation of gravitational waves produced by a strongly gravitating sou
 rce. In the presence of multiple sources\, the impulsive waves eventually 
 interact\, and it is interesting to study this interaction. \n From the pe
 rspectives of PDEs\, impulsive gravitational waves are low regularity solu
 tions of the Einstein equations\, seen as a system of non-linear wave equa
 tions\; thus even well-posedness of the initial value problem is not clear
  a priori.\n\nTremendous progress has been recently made in the understand
 ing of low regularity solutions of the Einstein equations. It is remarkabl
 e that similar techniques can be applied to very different problems\, such
  as the formation of Black Holes\, the behaviour of high-frequency space-t
 imes or the interaction of impulsive gravitational waves.\n\nIn this talk\
 , I will survey several low-regularity physical phenomena and explain the 
 underlying techniques from the perspective of PDEs. I will then discuss im
 pulsive gravitational waves and present a new local existence result for s
 olutions featuring three gravitational waves or more.\n\nThe talk will mai
 nly emphasise PDE-related aspects\, and no prior exposure to General Relat
 ivity will be assumed. This is joint work with Jonathan Luk.
LOCATION:MR14\, Centre for Mathematical Sciences
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