标题： Kerr时空引力扰动的新规范 II：施瓦茨希尔德的线性稳定性再审视 显示英文标题

标题： A new gauge for gravitational perturbations of Kerr spacetimes II: The linear stability of Schwarzschild revisited

摘要： 我们提出了一个关于施瓦茨希尔德解在引力扰动下线性稳定性的新证明。 我们的方法采用了在\cite{benomio_kerr}的新几何规范下的线性化引力系统，并专门用于$|a|=0$情况。 该证明根本上依赖于系统中传输方程的新结构。 事实上，虽然利用了两个规范不变的线性化量通过自旋$\pm 2$鹤克利方程的已知解耦，但我们更充分地利用了红移传输方程及其稳定性质来控制系统的规范相关部分。 结果表明，初始数据的规范归一化足以建立系统中所有线性化量的轨道稳定性和渐近稳定性。 未来规范归一化的缺失是在线性稳定性分析中，在由传输方程支配的几何规范下的黑洞时空的一个新元素。 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（双零）规范来建立整个系统的渐近稳定性。 显示英文摘要

摘要： 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.