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CATEGORIES:DAMTP Friday GR Seminar
SUMMARY:Islands of stability and recurrence times in AdS -
Stephen Green\, Perimeter Institute
DTSTART;TZID=Europe/London:20151127T130000
DTEND;TZID=Europe/London:20151127T140000
UID:TALK61393AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/61393
DESCRIPTION:This talk is concerned with the stability of anti–
de Sitter (AdS) spacetime to spherically symmetric
perturbations of a real scalar field in general r
elativity. For small-amplitude initial data\, two
types of behavior have been observed numerically\,
depending on the initial data profile: collapse t
o a black hole via a turbulent cascade of energy\,
and noncollapse characterized by recurrences that
approach the initial state. In this talk\, I will
first introduce a two timescale approximation tha
t describes the leading nonlinear interactions for
small-amplitude perturbations\, and is suitable f
or studying the weakly turbulent instability of Ad
S---both noncollapsing and collapsing solutions. W
ithin this framework\, I will identify a large cla
ss of equilibrium solutions\, which are quasiperio
dic in time\, and I will show that they are stable
. I argue that these solutions represent "islands
of stability" in AdS and that recurrences observed
in generic noncollapsing solutions are orbits abo
ut these equilibria. Moreover\, the stability anal
ysis gives rise to the measured recurrence times.
Alternatively\, for initial data far from an equil
ibrium solution\, large amounts of energy are driv
en to high-frequency modes\, and the two timescale
approximation breaks down. Depending on the highe
r order dynamics of the full system\, this often s
ignals an imminent collapse to a black hole.
LOCATION:Pavilion B Potter Room (B1.19)
CONTACT:
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