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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

MPS-Authors

Ma,  Siyuan
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1708.07385.pdf
(Preprint), 869KB

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Citation

Ma, S. (2020). 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. Communications in Mathematical Physics, 377(3), 2489-2551. doi:10.1007/s00220-020-03777-2.


Cite as: http://hdl.handle.net/21.11116/0000-0006-7C1B-2
Abstract
This second part of the series treats spin $\pm2$ components (or extreme components) of the linearized gravitational perturbations (linearized gravity) in the exterior of a slowly rotating Kerr black hole, following the hierarchy introduced in our first part [15] on the Maxwell field. This hierarchy lies in the fact that for each of these two components defined in Kinnersley tetrad, the resulting equations by performing some first-order differential operator on it once and twice, together with the Teukolsky master equation, are in the form of an "inhomogeneous spin-weighted wave equation" (ISWWE) with different potentials and constitute a linear spin-weighted wave system. We then prove energy and integrated local energy decay (Morawetz) estimates for this type of ISWWE, and utilize them to achieve both a uniform bound of a positive definite energy and a Morawetz estimate for the regular extreme Newman-Penrose components defined in the regular Hawking-Hartle tetrad.