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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

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1708.07385.pdf

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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.