A scattering theory for the wave equation on kerr black hole exteriors

IF 1.3 1区数学 Q1 MATHEMATICS

Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2014-12-29 DOI:10.24033/asens.2358

Mihalis Dafermos, I. Rodnianski, Yakov Shlapentokh-Rothman

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引用次数: 59

Abstract

We develop a definitive physical-space scattering theory for the scalar wave equation on Kerr exterior backgrounds in the general subextremal case |a|

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克尔黑洞外部波动方程的散射理论

对于一般亚极值情况下Kerr外背景下的标量波动方程，我们建立了一个确定的物理空间散射理论。特别地，我们证明了“散射态的存在唯一性”和“渐近完备性”所对应的结果，并进一步证明了将过去视界和过去零无穷辐射场映射到未来视界和未来零无穷辐射场的“散射矩阵”是一个有界算子。后者允许我们给出超辐射反射的时域理论。散射矩阵的有界性特别表明，与入射有限能量波包有关的解在过零无穷远处的最大放大是有界的。在频率方面，这对应于一种新的说法，即适当归一化的反射系数和透射系数是均匀有界的，与频率参数无关。我们进一步证明，超辐射反射确实放大了上述合适波包辐射到未来零无穷大的能量。这些结果充分利用了我们最近证明的一个改进[M]。Dafermos, I. Rodnianski和Y. Shlapentokh-Rothman, Kerr外时空上波动方程解的衰减:有界性的完全次极值情形[a]

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来源期刊

Annales Scientifiques De L Ecole Normale Superieure 数学-数学

CiteScore

3.00

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics. Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition. The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.

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