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CATEGORIES:DAMTP Friday GR Seminar
SUMMARY:Scattering of three impulsive gravitational waves
and other low regularity problems - Maxime Van De
Moortel (DPMMS and Stanford)
DTSTART;TZID=Europe/London:20181109T130000
DTEND;TZID=Europe/London:20181109T140000
UID:TALK112039AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/112039
DESCRIPTION:An impulsive gravitational wave is a weak solution
of the Einstein equation\, which models gravitati
onal waves emanating from a strongly gravitating s
ource. In the presence of multiple sources\, the i
mpulsive waves eventually interact transversally a
nd it is interesting to study their scattering.\n\
nThe interaction of two general impulsive waves ha
s been understood locally in the seminal work of L
uk and Rodnianski. They prove that non-linear sing
ularities do not occur in the scattering\, in the
sense that space-time stays smooth away from the t
wo waves immediately after the interaction.\n\nImp
ulsive gravitational waves belong to the class of
low regularity space-times\, which appear in many
interesting topics of classical General Relativity
such as the formation of trapped surfaces\, the s
tructure of Black Hole interiors and high-frequenc
y metrics. In fact\, the techniques used to addres
s two impulsive waves by Luk and Rodnianski have f
ound spectacular applications to all the above-men
tioned problems.\n\nHowever\, the case where three
or more impulsive waves interact transversally is
not covered by earlier work. The methods of Luk-R
odnianski do not apply in this case and one conjec
turally expects a qualitatively different behaviou
r. I will present a new local existence and stabil
ity result for U(1) polarised Cauchy data featurin
g three impulsive gravitational waves of small amp
litude propagating towards each other. This result
establishes a framework to subsequently understan
d the non-linear singularity of three waves\, and
eventually the scattering of more singular solutio
ns.\n\nThis is joint work with Jonathan Luk.
LOCATION:Pavilion B Potter Room (B1.19)
CONTACT:
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