实轴模式稳定性
Mode stability on the real axis
摘要：
在实频率的情况下，证明了Whiting（1989）关于Teukolsky方程的模式稳定性结果的推广。本文的主要结果指出，一个分离的解决方案Teukolsky方程管理的无质量测试场的克尔时空，这是纯粹的外向在无穷远，并纯粹进入的视界，必须消失。这有一个结果，即对于实频率，径向Teukolsky方程的基本解是线性独立的，它们分别是在视界处的纯输入解和在无穷远处的纯输出解。这一事实产生了一个表示公式的解决方案的非齐次Teukolsky方程。
英文摘要：
A generalization of the mode stability result of Whiting (1989) for the Teukolsky equation is proved for the case of real frequencies. The main result of the paper states that a separated solution of the Teukolsky equation governing massless test fields on the Kerr spacetime, which is purely outgoing at infinity, and purely ingoing at the horizon, must vanish. This has the consequence, that for real frequencies, there are linearly independent fundamental solutions of the radial Teukolsky equation which are purely ingoing at the horizon, and purely outgoing at infinity, respectively. This fact yields a representation formula for solutions of the inhomogenous Teukolsky equation.
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