Physical-space estimates for axisymmetric waves on extremal Kerr spacetime (joint with Elena Giorgi)
Published in Journal of Functional Analysis, Volume 287, Issue 12, Article 110668, 2022
We study axisymmetric solutions to the wave equation on extremal Kerr backgrounds and obtain integrated local energy decay (or Morawetz estimates) through an analysis conducted *exclusively in physical space*. The boundedness of the energy and Morawetz estimates for axisymmetric waves in extremal Kerr were first obtained by Aretakis through frequency-localized currents, which were used to express the trapping degeneracy. Here, we extend to extremal Kerr a method introduced by Stogin in the sub-extremal case, simplifying Aretakis' derivation of Morawetz estimates through purely classical currents.