论文标题
Teukolsky方程式在Kerr上的有界和衰减
Boundedness and decay for the Teukolsky equation on Kerr in the full subextremal range $|a|<M$: frequency space analysis
论文作者
论文摘要
本文是有关旋转$ \ pm 1 $的Teukolsky方程的系列中的第一个，在全部kerr背景的旋转$ \ pm 2 $中，参数$ | a | <m $。在本文中，我们研究了Dafermos，Holzegel和Rodnianski引入的转换方程系统的固定频率解，获得了分离参数中均匀的估计值。我们的结果的推论是在该系列的第二篇论文中列出的，它是Teukolsky方程在次级KERR上的溶液在定期初始数据引起的次数Kerr上保持界限，并且会及时衰减。这是在电磁和重力扰动下建立KERR的完整线性稳定性的关键步骤。我们的估计还可以应用于理解Teukolsky方程的更精致的特征，例如它们的散射特性。
This paper is the first of a series regarding the Teukolsky equation of spin $\pm 1$ and spin $\pm 2$ on Kerr backgrounds in the full subextremal range of parameters $|a|<M$. In the present paper, we study fixed frequency solutions of the transformed system of equations introduced by Dafermos, Holzegel and Rodnianski, obtaining estimates which are uniform in the separation parameters. A corollary of our result, to be laid out in the second paper of the series, is that solutions of the Teukolsky equation on subextremal Kerr arising from regular initial data remain bounded and decay in time. This is a key step in establishing the full linear stability of Kerr under electromagnetic and gravitational perturbations. Our estimates can also be applied to understanding more delicate features of the Teukolsky equation, such as their scattering properties.
