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SUMMARY:Time-translation invariance of scattering maps and blue-shift inst
 abilities on Kerr black hole spacetimes - Yakov Shlapentokh-Rothman (Princ
 eton)
DTSTART:20160222T150000Z
DTEND:20160222T160000Z
UID:TALK63155@talks.cam.ac.uk
CONTACT:Prof. Mihalis Dafermos
DESCRIPTION:The goal of this talk will be to provide an elementary\, unifi
 ed treatment of two distinct blue-shift instabilities for the scalar wave 
 equation on a fixed Kerr black hole background: the celebrated blue-shift 
 at the Cauchy horizon (familiar from the strong cosmic censorship conjectu
 re) and the time-reversed red-shift at the event horizon (relevant in clas
 sical scattering theory). After a review of our recently developed scatter
 ing theory for the wave equation (joint work with Mihalis Dafermos and Igo
 r Rodnianski)\, we will present two theorems. The first theorem constructs
  solutions to the wave equation on Kerr spacetimes such that the radiation
  field along the future event horizon vanishes and the radiation field alo
 ng future null infinity decays at an arbitrarily fast polynomial rate\, ye
 t\, the local energy of the solution is infinite near any point on the fut
 ure event horizon. The second theorem constructs solutions to the wave equ
 ation on rotating Kerr spacetimes such that the radiation field along the 
 past event horizon (extended into the black hole) vanishes and the radiati
 on field along past null infinity decays at an arbitrarily fast polynomial
  rate\, yet\, the local energy of the solution is infinite near any point 
 on the Cauchy horizon. This is joint work with Mihalis Dafermos.
LOCATION:CMS\, MR13
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