Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime

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Abstract

We give a quantitative refinement and simple proofs of mode stability type statements for the wave equation on Kerr backgrounds in the full sub-extremal range (|a| <  M). As an application, we are able to quantitatively control the energy flux along the horizon and null infinity and establish integrated local energy decay for solutions to the wave equation in any bounded-frequency regime.

Original languageEnglish (US)
Pages (from-to)289-345
Number of pages57
JournalAnnales Henri Poincare
Volume16
Issue number1
DOIs
StatePublished - Jan 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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