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SUMMARY:Impulsive gravitational waves - Jonathan Luk (Princeton)
DTSTART:20111024T150000Z
DTEND:20111024T160000Z
UID:TALK34093@talks.cam.ac.uk
CONTACT:Jonathan Ben-Artzi
DESCRIPTION:We consider spacetimes satisfying the vacuum Einstein equation
 s with impulsive gravitational waves without symmetry assumptions. These a
 re spacetimes such that the Riemann curvature tensor has a delta singulari
 ty across a null hypersurface. We prove local existence and uniqueness for
  the characteristic initial value problem with initial data that has a del
 ta singularity in the curvature tensor. A precise description of the propa
 gation of singularity is also given. The proof introduces a new type of en
 ergy estimates for the vacuum Einstein equations\, allowing the $L^2$ norm
  of some components of the curvature tensor to be infinite. The new estima
 te allows us to prove local existence for a general class of initial data 
 which is non-regular along a null direction. We will discuss extensions of
  this theorem\, which can be applied to understand colliding impulsive gra
 vitational waves and the formation of trapped surface. This is joint work 
 with I. Rodnianski.
LOCATION:CMS\, MR15
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