Mode Stability for the Teukolsky Equation on Extremal and Subextremal Kerr Spacetimes
Mode Stability for the Teukolsky Equation on Extremal and Subextremal Kerr Spacetimes
复制标题
极值和次极值克尔时空 Teukolsky 方程的模式稳定性
DOI：
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发表时间：
2019
影响因子：
2.4
通讯作者：
Rita Teixeira da Costa
中科院分区：
文献类型：
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作者：
Rita Teixeira da Costa
证明了Kerr黑洞时空上Teukolsky方程的实轴上既不存在指数增长模，也不存在亚极值情况下的模。我们还给出了模式稳定性的定量修正。作为直接应用，我们证明了散射问题的透射系数和反射系数在不包括零频率和超辐射阈值的任何紧凑的实频率集合中是有界的，与黑洞的特定角动量无关。虽然在次极值情况下这些结果是已知的，但极值情况更复杂，并且一直是一个开放的问题。我们的结果是轴对称外的第一个结果，可以作为理解极值Kerr黑洞上Teukolsky方程通解的有界性、散射和衰变性质的初步步骤。
We prove that there are no exponentially growing modes nor modes on the real axis for the Teukolsky equation on Kerr black hole spacetimes, both in the extremal and subextremal case. We also give a quantitative refinement of mode stability. As an immediate application, we show that the transmission and reflection coefficients of the scattering problem are bounded, independently of the specific angular momentum of the black hole, in any compact set of real frequencies excluding zero frequency and the superradiant threshold. While in the subextremal setting these results were known previously, the extremal case is more involved and has remained an open problem. Ours are the first results outside axisymmetry and could serve as a preliminary step towards understanding boundedness, scattering and decay properties of general solutions to the Teukolsky equation on extremal Kerr black holes.
影响因子：
3.7
作者：
Dafermos, Mihalis;Holzegel, Gustav;Rodnianski, Igor
通讯作者：
Rodnianski, Igor