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SUMMARY:The global stability of the Minkowski spacetime solution to the Ei
 nstein-nonlinear electromagnetic system in wave coordinates - Jared Speck 
 (Princeton)
DTSTART:20110404T150000Z
DTEND:20110404T160000Z
UID:TALK30622@talks.cam.ac.uk
CONTACT:Prof. Mihalis Dafermos
DESCRIPTION:The Einstein-nonlinear electromagnetic system is a coupling of
  the Einstein field equations of general relativity to nonlinear electroma
 gnetic field equations. In this talk\, I will discuss the family of covari
 ant electromagnetic models that satisfy the following criteria: i) they ar
 e derivable from a sufficiently regular Lagrangian\, ii) they reduce to th
 e familiar Maxwell model in the weak-field limit\, and iii) their correspo
 nding energy-momentum tensors satisfy the dominant energy condition. I wil
 l mention several specific electromagnetic models that are of interest to 
 researchers working in the foundations of physics. I will then discuss my 
 main result\, which is a proof of the global nonlinear stability of the 1 
 + 3 dimensional Minkowski spacetime solution to the coupled system. This s
 tability result is a consequence of a small-data global existence result f
 or a reduced system of equations that is equivalent to the original system
  in a wave coordinate gauge. The analysis of the spacetime metric componen
 ts is based on a framework recently developed by Lindblad and Rodnianski\,
  which allows one to derive suitable estimates for tensorial systems of qu
 asilinear wave equations with nonlinearities that satisfy the weak null co
 ndition. The analysis of the electromagnetic fields\, which satisfy quasil
 inear first-order equations\, is based on an extension of a geometric ener
 gy-method framework developed by Christodoulou\, together with a collectio
 n of pointwise decay estimates for the Faraday tensor that I develop. Thro
 ughout the analysis\, I work directly with the electromagnetic fields\, th
 us avoiding the introduction of electromagnetic potentials.
LOCATION:CMS\, MR13
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