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CATEGORIES:Geometric Analysis and Partial Differential Equati
ons seminar
SUMMARY:Time-translation invariance of scattering maps and
blue-shift instabilities on Kerr black hole space
times - Yakov Shlapentokh-Rothman (Princeton)
DTSTART;TZID=Europe/London:20160222T150000
DTEND;TZID=Europe/London:20160222T160000
UID:TALK63155AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/63155
DESCRIPTION:The goal of this talk will be to provide an elemen
tary\, unified treatment of two distinct blue-shif
t instabilities for the scalar wave equation on a
fixed Kerr black hole background: the celebrated b
lue-shift at the Cauchy horizon (familiar from the
strong cosmic censorship conjecture) and the time
-reversed red-shift at the event horizon (relevant
in classical scattering theory). After a review o
f our recently developed scattering theory for the
wave equation (joint work with Mihalis Dafermos a
nd Igor Rodnianski)\, we will present two theorems
. The first theorem constructs solutions to the wa
ve equation on Kerr spacetimes such that the radia
tion field along the future event horizon vanishes
and the radiation field along future null infinit
y decays at an arbitrarily fast polynomial rate\,
yet\, the local energy of the solution is infinite
near any point on the future event horizon. The s
econd theorem constructs solutions to the wave equ
ation on rotating Kerr spacetimes such that the ra
diation field along the past event horizon (extend
ed into the black hole) vanishes and the radiation
field along past null infinity decays at an arbit
rarily fast polynomial rate\, yet\, the local ener
gy of the solution is infinite near any point on t
he Cauchy horizon. This is joint work with Mihalis
Dafermos.
LOCATION:CMS\, MR13
CONTACT:Prof. Mihalis Dafermos
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