This second part of the series treats spin $$\pm 2$$ ± 2 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 $$\pm 2$$ ± 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.

中文翻译：

---

缓慢旋转的克尔黑洞 II 外部自旋场极端分量的均匀能量界和莫拉维茨估计：线性化重力

该系列的第二部分处理了缓慢旋转的克尔黑洞外部线性化重力的自旋 $$\pm 2$$ ± 2 分量（或极端分量），它们满足 Teukolsky 主方程。对于这两个分量中的每一个，在执行一次和两次一阶微分算子后，得到的方程与 Teukolsky 主方程本身一起构成了线性自旋加权波系统。通过处理该系统证明了自旋 $$\pm 2$$ ± 2 分量的能量和 Morawetz 估计。这是解决缓慢旋转克尔度量的线性稳定性的联合工作的第一步（Andersson 等人在 Kerr 时空线性化重力的稳定性，arXiv:1903.03859，2019 年）。