论文标题
在Kerr的扰动中构建GCM Hypersurfaces
Construction of GCM hypersurfaces in perturbations of Kerr
论文作者
论文摘要
这是\ cite {ks：kerr1}在Kerr扰动中的一般协变量调制过程（GCM）过程中的随访。在本文中，我们构建了GCM Hypersurfaces，在\ cite {ks：main}中延长GCM的可允许的空间中起着核心作用，在\ cite {ks：main}中，衰减估计值是在kerr家族的非线性稳定性的$ | a | a | \ ll m $的非线性稳定性的背景下得出的。如\ cite {ks}中一样，构建GCM Hypersurfaces的核心思想是通过求解ODE系统来加以$ 1 $ - \ cit {ks：kerr1}的GCM球的参数家族。本文的目的是摆脱\ cite {ks}中引入的GCM程序中的对称限制，从而消除将结果扩展到Kerr家族的完全稳定性证明的基本障碍。
This is a follow-up of \cite{KS:Kerr1} on the general covariant modulated (GCM) procedure in perturbations of Kerr. In this paper, we construct GCM hypersurfaces, which play a central role in extending GCM admissible spacetimes in \cite{KS:main} where decay estimates are derived in the context of nonlinear stability of Kerr family for $|a|\ll m$. As in \cite{KS}, the central idea of the construction of GCM hypersurfaces is to concatenate a $1$--parameter family of GCM spheres of \cite{KS:Kerr1} by solving an ODE system. The goal of this paper is to get rid of the symmetry restrictions in the GCM procedure introduced in \cite{KS} and thus remove an essential obstruction in extending the results to a full stability proof of the Kerr family.
