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arXiv · 1708.07385

Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole II: linearized gravity

Siyuan Ma
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Abstract

This second part of the series treats spin $\pm2$ components (or extreme components), that satisfy the Teukolsky master equation, of the linearized gravity in the exterior of a slowly rotating Kerr black hole. For each of these two components, after performing a first-order differential operator once and twice, the resulting equations together with the Teukolsky master equation itself constitute a linear spin-weighted wave system. An energy and Morawetz estimate for spin $\pm 2$ components is proved by treating this system. This is a first step in a joint work (Andersson et al. in Stability for linearized gravity on the Kerr spacetime, arXiv:1903.03859, 2019) in addressing the linear stability of slowly rotating Kerr metrics.

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Siyuan Ma. 2017-08-23. Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole II: linearized gravity. https://doi.org/10.1007/s00220-020-03777-2

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