论文标题
波动方程估计和缓慢旋转的Kerr黑色孔的非线性稳定性
Wave equations estimates and the nonlinear stability of slowly rotating Kerr black holes
论文作者
论文摘要
这是我们对小角动量的非线性稳定性证明的最后一部分，即$ | a | a |/m \ ll 1 $，其中我们处理完成项目所需的非线性波类型估计值。更确切地说，我们为定理M1和M2提供了完整的证明，以及定理M8的曲率估计值，在\ cite {KS：Kerr}的第3.7.1和9.4.7节中没有证明。我们的程序基于一种新的一般兴趣形式主义（在本工作的第一部分中详细介绍），该形式扩展了Minkowski Space稳定性的一种。与\ cite {ks：kerr}和gcm papers \ cite \ cite {ks-gcm1}，\ cite {ks-gcm2}，\ cite {shen}一起完成了\ cite {ks：ks kerr}的主要理论的证明。
This is the last part of our proof of the nonlinear stability of the Kerr family for small angular momentum, i.e $|a|/m\ll 1$, in which we deal with the nonlinear wave type estimates needed to complete the project. More precisely we provide complete proofs for Theorems M1 and M2 as well the curvature estimates of Theorem M8, which were stated without proof in sections 3.7.1 and 9.4.7 of \cite{KS:Kerr}. Our procedure is based on a new general interest formalism (detailed in Part I of this work), which extends the one used in the stability of Minkowski space. Together with \cite{KS:Kerr} and the GCM papers \cite{KS-GCM1}, \cite{KS-GCM2}, \cite{Shen}, this work completes proof of the Main Theorem stated in Section 3.4 of \cite{KS:Kerr}.
