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.
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Communicated by James A. Isenberg.
This work was partially supported by NSF Grant DMS-0943787.
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Shlapentokh-Rothman, Y. Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime. Ann. Henri Poincaré 16, 289–345 (2015). https://doi.org/10.1007/s00023-014-0315-7
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DOI: https://doi.org/10.1007/s00023-014-0315-7