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SUMMARY:The Stability of the Euler-Einstein system with a positive Cosmolo
 gical Constant - Jared Speck (DPMMS)
DTSTART:20100426T120000Z
DTEND:20100426T130000Z
UID:TALK24316@talks.cam.ac.uk
CONTACT:Tasos Avgoustidis
DESCRIPTION:The Euler-Einstein system models the evolution of a dynamic sp
 acetime containing a perfect fluid. In this talk\, I will discuss the non
 linear stability of the Friedmann-Lemaˆıtre-Robertson-Walker family of b
 ackground cosmological solutions to the Euler-Einstein system in 1 + 3 dim
 ensions with a positive cosmological constant Λ. The background solutions
  describe an initially uniform quiet fluid of positive energy density evo
 lving in a spacetime undergoing accelerated expansion. The main result is 
 a proof that under the equation of state p = cs^2^ ρ\, 0 < cs^2^ < 1/3\, 
 the  \nbackground solutions are globally future-stable under small perturb
 ations. In particular\, the perturbed spacetimes\, which have the topologi
 cal structure \n[0\, ∞) × T3 \, are future causally geodesically comple
 te. The results I will present are extensions of previous joint work with 
 Igor Rodnianski\, which covered the case of an irrotational fluid\, and o
 f work by Hans Ringstrom on the Einstein-non-linear-scalar-field system.\
 nMathematically\, the main result is a proof of small-data global existenc
 e for a modified version of the Euler-Einstein equations that are equival
 ent to the un-modified equations. The proof is based on the vectorfield 
 method of Christodoulou and Klainerman.\n\nIt is of special interest to no
 te that the behavior of the fluid in an exponentially expanding spacetime
  differs drastically from the case of flat spacetime. More specifically\
 , Christodoulou has recently shown that on the Minkowski space background\
 , data arbitrarily close to that of an initially uniform quiet fluid stat
 e can lead to solutions that form shocks. In view of this fact\, we remark
  that the proof of our result can be used to show the following: exponenti
 ally expanding spacetime backgrounds can prevent the formation of shocks.
LOCATION:CMS\, Pav.B\, CTC Common Room (B1.19)
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