论文标题
极端Kerr时空上轴对称波的物理空间估计值
Physical-space estimates for axisymmetric waves on extremal Kerr spacetime
论文作者
论文摘要
我们通过分析\ textit {独家在物理空间}来研究极端KERR背景上波方程的轴对称解，并获得局部能量衰减（或Morawetz估计）。首先通过Aretakis构建频率 - 重新定位的电流，特别是用来表达捕获脱落的频率，首先通过Aretakis获得了极端Kerr中轴对称波的能量和摩拉维兹估计的界限。在这里，我们扩展到了极端Kerr，一种在亚超级情况下引入的方法，通过纯粹的经典电流简化了Aretakis对Morawetz估计的推导。
We study axisymmetric solutions to the wave equation on extremal Kerr backgrounds and obtain integrated local energy decay (or Morawetz estimates) through an analysis \textit{exclusively in physical-space}. Boundedness of the energy and Morawetz estimates for axisymmetric waves in extremal Kerr were first obtained by Aretakis through the construction of frequency-localized currents used in particular to express the trapping degeneracy. Here we extend to extremal Kerr a method introduced by Stogin in the sub-extremal case, simplifying Aretakis' derivation of Morawetz estimates through purely classical currents.
