Physical-space estimates for axisymmetric waves on extremal Kerr spacetime

Fuente: arXiv
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Hauptverfasser: Giorgi, Elena, Wan, Jingbo
Format: Preprint
Veröffentlicht: 2022
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author Giorgi, Elena
Wan, Jingbo
author_facet Giorgi, Elena
Wan, Jingbo
contents We study axisymmetric solutions to the wave equation on extremal Kerr backgrounds and obtain integrated local energy decay (or Morawetz estimates) through an analysis \textit{exclusively in physical-space}. Boundedness of the energy and Morawetz estimates for axisymmetric waves in extremal Kerr were first obtained by Aretakis through the construction of frequency-localized currents used in particular 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.
format Preprint
id arxiv_https___arxiv_org_abs_2212_13164
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Physical-space estimates for axisymmetric waves on extremal Kerr spacetime
Giorgi, Elena
Wan, Jingbo
Analysis of PDEs
General Relativity and Quantum Cosmology
Mathematical Physics
Differential Geometry
We study axisymmetric solutions to the wave equation on extremal Kerr backgrounds and obtain integrated local energy decay (or Morawetz estimates) through an analysis \textit{exclusively in physical-space}. Boundedness of the energy and Morawetz estimates for axisymmetric waves in extremal Kerr were first obtained by Aretakis through the construction of frequency-localized currents used in particular 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.
title Physical-space estimates for axisymmetric waves on extremal Kerr spacetime
topic Analysis of PDEs
General Relativity and Quantum Cosmology
Mathematical Physics
Differential Geometry
url https://arxiv.org/abs/2212.13164