论文标题
Schwarzschild Black Hole II的线性重力的散射理论II：完整系统
A Scattering Theory for Linearised Gravity on the Exterior of the Schwarzschild Black Hole II: The Full System
论文作者
论文摘要
我们在双零仪表中的Schwarzschild背景上为线性化的爱因斯坦方程构建了散射理论。我们基于第i \ cite {mas20}的结果，在那里我们使用了雷格（Regge）所享有的节能 - 与Schwarzschild背景平稳性相关的轮毂方程式来构建Teukolsky方程的Spin $ \ pm2 $的散射理论。现在，我们将第I部分的散射理论扩展到了整个线性化的爱因斯坦方程组的系统，它是将其视为一种传输方程系统，该系统是通过对Teukolsky方程的解决方案来提出的，从而导致希尔伯特太空均等的呈相构态在有限的能量初始数据和相应的散射状态之间的最初和散射状态下的散射状态之间的相应空间之间。作为推论，我们表明，对于在过去和将来的无效无穷大范围内都符合债券差异的解决方案，过去和将来的线性记忆与抗虫图相关。
We construct a scattering theory for the linearised Einstein equations on a Schwarzschild background in a double null gauge. We build on the results of Part I \cite{Mas20}, where we used the energy conservation enjoyed by the Regge--Wheeler equation associated with the stationarity of the Schwarzschild background to construct a scattering theory for the Teukolsky equations of spin $\pm2$. We now extend the scattering theory of Part I to the full system of linearised Einstein equations by treating it as a system of transport equations which is sourced by solutions to the Teukolsky equations, leading to Hilbert space-isomorphisms between spaces of finite energy initial data and corresponding spaces of scattering states under suitably chosen gauge conditions on initial and scattering data. As a corollary, we show that for a solution which is Bondi-normalised at both past and future null infinity, past and future linear memories are related by an antipodal map.
