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SUMMARY:Islands of stability and recurrence times in AdS - Stephen Green\,
  Perimeter Institute
DTSTART:20151127T130000Z
DTEND:20151127T140000Z
UID:TALK61393@talks.cam.ac.uk
CONTACT:43345
DESCRIPTION:This talk is concerned with the stability of anti–de Sitter 
 (AdS) spacetime to spherically symmetric perturbations of a real scalar fi
 eld in general relativity. For small-amplitude initial data\, two types of
  behavior have been observed numerically\, depending on the initial data p
 rofile: collapse to a black hole via a turbulent cascade of energy\, and n
 oncollapse characterized by recurrences that approach the initial state. I
 n this talk\, I will first introduce a two timescale approximation that de
 scribes the leading nonlinear interactions for small-amplitude perturbatio
 ns\, and is suitable for studying the weakly turbulent instability of AdS-
 --both noncollapsing and collapsing solutions. Within this framework\, I w
 ill identify a large class of equilibrium solutions\, which are quasiperio
 dic in time\, and I will show that they are stable. I argue that these sol
 utions represent "islands of stability" in AdS and that recurrences observ
 ed in generic noncollapsing solutions are orbits about these equilibria. M
 oreover\, the stability analysis gives rise to the measured recurrence tim
 es. Alternatively\, for initial data far from an equilibrium solution\, la
 rge amounts of energy are driven to high-frequency modes\, and the two tim
 escale approximation breaks down. Depending on the higher order dynamics o
 f the full system\, this often signals an imminent collapse to a black hol
 e.
LOCATION:Pavilion B Potter Room (B1.19)
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