论文标题
Teukolsky方程的模式稳定性在Kerr-anti-de保姆上
Mode stability for the Teukolsky equations on Kerr-anti-de Sitter spacetimes
论文作者
论文摘要
我们证明，在所有$（3+1）$ -Dimensional subsextremal Kerr-anti-de Sitter SpaceTimes上，没有针对Teukolsky方程的真实模式的非平稳（关于Hawking Vectorfield）的非平稳性解决方案。我们进一步证明，如果黑洞参数满足霍金 - 真实界限，并且$ \ left | a \ sqrt { - λ} \ right | <\ frac {\ frac {\ sqrt {3}}} $不存在固定解决方案。我们以模式稳定性的陈述为结论，该声明预言了界限和通用解决方案的衰减估计，这些估计将在单独的论文中得到证明。我们的边界条件是固定无穷大的标准类别的标准条件，并导致两个Teukolsky方程的耦合。证明依赖于将Teukolsky-Starobinsky身份与耦合边界条件相结合。在固定案例中，证明利用椭圆估计值，如果违反了鹰派界限，则失败。这与该政权预期的超级不稳定性一致。
We prove that there are no non-stationary (with respect to the Hawking vectorfield) real mode solutions to the Teukolsky equations on all $(3+1)$-dimensional subextremal Kerr-anti-de Sitter spacetimes. We further prove that stationary solutions do not exist if the black hole parameters satisfy the Hawking-Reall bound and $\left|a\sqrt{-Λ}\right|<\frac{\sqrt{3}}{20}$. We conclude with the statement of mode stability which preludes boundedness and decay estimates for general solutions which will be proven in a separate paper. Our boundary conditions are the standard ones which follow from fixing the conformal class of the metric at infinity and lead to a coupling of the two Teukolsky equations. The proof relies on combining the Teukolsky-Starobinsky identities with the coupled boundary conditions. In the stationary case the proof exploits elliptic estimates which fail if the Hawking-Reall bound is violated. This is consistent with the superradiant instabilities expected in that regime.
