arXiv 0901.33162009-01-21gr-qc

Kerr时空非线性微扰“非常外部区域”的剥离

The peeling in the "very external region" of non linear perturbations of the Kerr spacetime

Francesco Nicolò

摘要：

设初始数据度规$\overline{g}$是Kerr时空的$Σ_0$上的诱导度规，它位于以原点为中心的球$B_{R_0}$之外（具有质量$M$和角动量$J$，其比值$J/M$取决于$R_0$的大小）加上小的修正，其在类空无穷远处的衰减速度比$r^{-3}$快;设在同一区域中，对称张量$\overline{k}$是Kerr时空的第二基本形式加上在类空无穷远处衰减比$r^{-4}$快的小修正，令$\overline{g}$和$\overline{k}$满足约束方程。然后，利用\cite{Ch-Kl:book}和\cite{Kl-Ni:book}以前的结果，在$B_{R_0}$的影响区域之外的全局时空的外部区域的全局存在性如下。在这个外部区域中，黎曼张量的各个分量沿着与“剥离定理”一致的出射零方向衰减。

英文摘要：

Let an initial data metric $\overline{g}$ be, outside a ball $B_{R_0}$ centered in the origin, the induced metric on $Σ_0$ of a Kerr spacetime (with a mass $M$ and angular momentum $J$ whose ratio, $J/M$, depends on the size of $R_0$) plus small corrections which decay at spacelike infinity faster than $r^{-3}$; let, in the same region, a symmetric tensor $\overline{k}$ be the second fundamental form of the Kerr spacetime plus small corrections which decay at spacelike infinity faster than $r^{-4}$, let $\overline{g}$ and $\overline{k}$ satisfy the constraint equations. Then, using the previous results of \cite{Ch-Kl:book} and \cite{Kl-Ni:book}, the global existence of the external region of a global spacetime, outside the region of influence of $B_{R_0}$ follows. In this external region the various components of the Riemann tensor decay along the outgoing null directions in agreement with the "Peeling Theorem".

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文