Construction of GCM Hypersurfaces in Perturbations of Kerr

IF 2.4 1区 数学 Q1 MATHEMATICS Annals of Pde Pub Date : 2023-05-30 DOI:10.1007/s40818-023-00152-x
Dawei Shen
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引用次数: 1

Abstract

This is a follow-up of [5] 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 [7] where decay estimates are derived in the context of nonlinear stability of Kerr family for \(|a|\ll m\). As in [4], the central idea of the construction of GCM hypersurfaces is to concatenate a 1–parameter family of GCM spheres of [5] by solving an ODE system. The goal of this paper is to get rid of the symmetry restrictions in the GCM procedure introduced in [4] and thus remove an essential obstruction in extending the results to a full stability proof of the Kerr family.

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Kerr摄动下GCM超曲面的构造
这是[5]在Kerr扰动中的一般协变调制(GCM)过程的后续。在本文中,我们构造了GCM超曲面,它在[7]中扩展GCM容许时空中起着核心作用,其中在Kerr族的非线性稳定性的背景下导出了\(|a|\ll m\)的衰变估计。与[4]中一样,构造GCM超曲面的中心思想是通过求解ODE系统来连接[5]的GCM球的1参数族。本文的目标是摆脱[4]中引入的GCM过程中的对称性限制,从而消除将结果扩展到Kerr族的完全稳定性证明的一个重要障碍。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Annals of Pde
Annals of Pde Mathematics-Geometry and Topology
CiteScore
3.70
自引率
3.60%
发文量
22
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