标题： 施瓦茨希尔德时空在极化扰动下的全局非线性稳定性 显示英文标题

标题： Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations

摘要： 我们证明了在轴对称极化扰动下的施瓦茨希尔德时空的非线性稳定性，即满足渐近平坦$1+3$维洛伦兹度量的爱因斯坦真空方程的解，这些解具有一个与超曲面正交的空间类的Killing向量场，并且该向量场具有闭合轨道。 在建立定量线性稳定性的最近15年取得的显著进展的基础上，本文引入了一系列新思想，其中我们强调了一般的协变调制（GCM）过程，该过程使我们能够动态地构造最终状态的质量中心框架。 最终状态的质量本身是通过相对于与质量中心框架相关的良好适应的叶状结构的已知霍金质量来跟踪的。 我们的工作是首次在一类非平凡扰动的限制类别中证明施瓦茨希尔德的非线性稳定性。 在很大程度上，对这类扰动的限制只是为了确保演化的最终状态是另一个施瓦茨希尔德空间。 因此，我们相信我们的方法可能适用于更一般的设置。 显示英文摘要

摘要： We prove the nonlinear stability of the Schwarzschild spacetime under axially symmetric polarized perturbations, i.e. solutions of the Einstein vacuum equations for asymptotically flat $1+3$ dimensional Lorentzian metrics which admit a hypersurface orthogonal spacelike Killing vectorfield with closed orbits. While building on the remarkable advances made in last 15 years on establishing quantitative linear stability, the paper introduces a series of new ideas among which we emphasize the general covariant modulation (GCM) procedure which allows us to construct, dynamically, the center of mass frame of the final state. The mass of the final state itself is tracked using the well known Hawking mass relative to a well adapted foliation itself connected to the center of mass frame. Our work here is the first to prove the nonlinear stability of Schwarzschild in a restricted class of nontrivial perturbations. To a large extent, the restriction to this class of perturbations is only needed to ensure that the final state of evolution is another Schwarzschild space. We are thus confident that our procedure may apply in a more general setting.