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Physical-space estimates for axisymmetric waves on extremal Kerr spacetime

Elena GiorgiJingbo Wan
Dec 2022
摘要
We study axisymmetric solutions to the wave equation on extremal Kerrbackgrounds and obtain integrated local energy decay (or Morawetz estimates)through an analysis \textit{exclusively in physical-space}. Boundedness of theenergy and Morawetz estimates for axisymmetric waves in extremal Kerr werefirst obtained by Aretakis through the construction of frequency-localizedcurrents used in particular to express the trapping degeneracy. Here we extendto extremal Kerr a method introduced by Stogin in the sub-extremal case,simplifying Aretakis' derivation of Morawetz estimates through purely classicalcurrents.
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