论文标题
Schwarzschild黑洞I：Teukolsky方程的线性重力的散射理论
A Scattering Theory for Linearised Gravity on the Exterior of the Schwarzschild Black Hole I: The Teukolsky Equations
论文作者
论文摘要
我们为Schwarzschild时空外部的自旋$ \ pm2 $ teukolsky方程构建了散射理论，这是开发双零仪表中线性化的爱因斯坦方程的散射理论的第一步。这是通过利用Dafermos，Holzegel和Rodnianski在[ARXIV：1601.06467]中使用的Chandrasekhar转换的物理空间版本来完成的，以证明Schwarzschild解决方案的线性稳定性。我们还谈到了Teukolsky-Starobinsky的通信，并在$+2 $和$ -2 $ Teukolsky方程的散射数据之间构建同构。这将使我们能够为满足旋转$+2 $和-2 $ -2 $ teukolsky方程的一对曲率组件提供其他混合散射语句，并通过Teukolsky-Starobinsky的身份连接，从而完全确定了对线性的Einstein方程的辐射自由度。
We construct a scattering theory for the spin $\pm2$ Teukolsky equations on the exterior of the Schwarzschild spacetime, as a first step towards developing a scattering theory for the linearised Einstein equations in double null gauge. This is done by exploiting a physical-space version of the Chandrasekhar transformation used by Dafermos, Holzegel and Rodnianski in [arxiv:1601.06467] to prove the linear stability of the Schwarzschild solution. We also address the Teukolsky-Starobinsky correspondence and construct an isomorphism between scattering data for the $+2$ and $-2$ Teukolsky equations. This will allow us to state an additional mixed scattering statement for a pair of curvature components satisfying the spin $+2$ and $-2$ Teukolsky equations and connected via the Teukolsky-Starobinsky identities, completely determining the radiating degrees of freedom of solutions to the linearised Einstein equations.
