论文标题
Schwarzschild Spacetime上的紧张波方程的共形散射理论
Conformal scattering theories for tensorial wave equations on Schwarzschild spacetime
论文作者
论文摘要
在本文中，我们建立了诸如张力fackerell-ipper和spin $ \ pm 1 $ teukolsky方程的紧张波方程的保形散射理论的结构。在我们的策略中，我们为从麦克斯韦方程和旋转$ \ pm 1 $ teukolsky方程获得的紧张fackerell-ipper方程构建了保形散射。我们的方法结合了Penrose的整形紧凑和满足张力的Fackerell-ipper方程的紧张场的能量衰减结果，以证明通过共形边界$ \ mathfrak { hypersurface $σ_0= \ left \ {t = 0 \ right \} $。我们将通过使用Hörmander在张力波方程的结果的概括来证明Goursat问题的良好性。通过使用Tensorial Fackerell-ipper方程的结果，我们将建立用于自旋$ \ pm 1 $ Teukolsky方程的保形散射的构建。
In this paper, we establish the constructions of conformal scattering theories for the tensorial wave equation such as the tensorial Fackerell-Ipser and the spin $\pm 1$ Teukolsky equations on Schwarzschild spacetime. In our strategy, we construct the conformal scattering for the tensorial Fackerell-Ipser equations which are obtained from the Maxwell equation and spin $\pm 1$ Teukolsky equations. Our method combines Penrose's conformal compactification and the energy decay results of the tensorial fields satisfying the tensorial Fackerell-Ipser equation to prove the energy equality of the fields through the conformal boundary $\mathfrak{H}^+\cup \scri^+$ (resp. $\mathfrak{H}^-\cup \scri^-$) and the initial Cauchy hypersurface $Σ_0 = \left\{ t=0 \right\}$. We will prove the well-posedness of the Goursat problem by using a generalization of Hörmander's results for the tensorial wave equations. By using the results for the tensorial Fackerell-Ipser equations we will establish the construction of conformal scattering for the spin $\pm 1$ Teukolsky equations.
