论文标题
Kerr Spacetimes II的重力扰动的新量表II：Schwarzschild的线性稳定性重新审视
A new gauge for gravitational perturbations of Kerr spacetimes II: The linear stability of Schwarzschild revisited
论文作者
论文摘要
我们提出了Schwarzschild解决方案对引力扰动的线性稳定性的新证明。我们的方法采用了\ cite {benomio_kerr}的新几何量表中的线性重力系统，专门针对$ | a | = 0 $ case。证明从根本上依赖于系统中传输方程的新结构。确实，在利用两个规格不变的线性量的众所周知的解耦中的同时，我们可以增强对红移的传输方程及其稳定属性的增强，以控制依赖系统的仪表部分。结果，初始数据规规范化足以建立系统中所有线性量的轨道和渐近稳定性。 未来量规标准化的缺失是由传输方程控制的几何仪表仪的线性稳定性分析的新元素。特别是，我们的方法简化了\ cite {dhr}的证明，该证明需要未来的归一化（双记号）仪表来为完整系统建立渐近稳定性。
We present a new proof of linear stability of the Schwarzschild solution to gravitational perturbations. Our approach employs the system of linearised gravity in the new geometric gauge of \cite{benomio_kerr}, specialised to the $|a|=0$ case. The proof fundamentally relies on the novel structure of the transport equations in the system. Indeed, while exploiting the well-known decoupling of two gauge invariant linearised quantities into spin $\pm 2$ Teukolsky equations, we make enhanced use of the red-shifted transport equations and their stabilising properties to control the gauge dependent part of the system. As a result, an initial-data gauge normalisation suffices to establish both orbital and asymptotic stability for all the linearised quantities in the system. The absence of future gauge normalisations is a novel element in the linear stability analysis of black hole spacetimes in geometric gauges governed by transport equations. In particular, our approach simplifies the proof of \cite{DHR}, which requires a future normalised (double-null) gauge to establish asymptotic stability for the full system.
