A proof of the instability of AdS for the Einstein-null dust system with an inner mirror
A proof of the instability of AdS for the Einstein-null dust system with an inner mirror
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DOI：
10.2140/apde.2020.13.1671
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发表时间：
2017-04
期刊：
影响因子：
2.2
通讯作者：
Georgios Moschidis
中科院分区：
文献类型：
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作者：
Georgios Moschidis
在2006年，Dafermos和Holzegel提出了所谓的AdS不稳定性猜想，指出存在任意小的扰动，AdS初始数据，在爱因斯坦真空方程的演化下，研究了这个系统在外部区域$\{r\ge r_{0}\}$上的演化。在我们的配套文件的结构的最大发展和柯西稳定性的一般初始数据在这种设置进行了研究。主要定理的陈述如下：我们构造了一个族的镜像半径$r_{0\displaystyle}>0$和初始数据$\mathcal{S}_{\displaystyle}$，$\mathcal\in（0，1]$，以适当的范数收敛到AdS初始数据，使得对于任何$\n>0$，最大发展$（\mathcal{M}_{\displaystyle\mathcal{M}_{\mathcal}，$\mathcal{S}_{\displaystyle $\mathcal{S}_{\displaystyle $\mathcal{S}_{\displaystyle $\mathcal{S}_{\mathcal {S}_{\mathcal}}$的g_{\displaystyle g_{\mathcal}}）$包含一个黑洞区域。我们的证明是基于纯粹的物理空间的论点。
In 2006, Dafermos and Holzegel formulated the so-called AdS instability conjecture, stating that there exist arbitrarily small perturbations to AdS initial data which, under evolution by the Einstein vacuum equations for $\Lambda0$ and study the evolution of this system on the exterior domain $\{r\ge r_{0}\}$. The structure of the maximal development and the Cauchy stability properties of general initial data in this setting are studied in our companion paper. The statement of the main theorem is as follows: We construct a family of mirror radii $r_{0\epsilon}>0$ and initial data $\mathcal{S}_{\epsilon}$, $\epsilon\in(0,1]$, converging to the AdS initial data in a suitable norm, such that, for any $\epsilon>0$, the maximal development $(\mathcal{M}_{\epsilon},g_{\epsilon})$ of $\mathcal{S}_{\epsilon}$ contains a black hole region. Our proof is based on purely physical space arguments.