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SUMMARY:The wave equation as a poor man's linearisation of the Einstein eq
 uations - Damon Civin
DTSTART:20130313T160000Z
DTEND:20130313T170000Z
UID:TALK43974@talks.cam.ac.uk
CONTACT:Amanda Stagg
DESCRIPTION:The Einstein field equations (EFE) can be written in harmonic\
 ncoordinates as a system of quasilinear wave equations. This allows for th
 e\nstudy of the (EFE) within the theory of hyperbolic PDE. In particular\,
  this\ncan be used to study well-posedness and stability of the (EFE) for 
 a large class of initial data.\n\nI'll focus on the linear wave equation\,
  which is the prototype hyperbolic PDE. It can also be viewed as a "poor m
 an's linearisation" of the (EFE). Therefore the study of boundedness and d
 ecay of solutions of the wave equation on a fixed black hole background ar
 e a first step towards stability of the background as a solution of the (E
 FE).\n\nI'll start off by discussing this "poor man's linearisation" and r
 ecalling what well-posedness means. We'll then move onto the highlights of
  the proof of well-posedness the Cauchy problem for the wave equation. \n\
 nAlong the way\, we'll run into some Sobolev spaces and energy estimates\,
  and I will try to convince you of their power and naturality. Time permit
 ting\,\nI'll discuss the heuristics of my work on the linear stability of 
 subextremal Kerr-Newman spacetimes.\n
LOCATION:CMS\, Potter Room (B1.19) 
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