论文标题
极端Reissner-Nordström时空的重力和电磁扰动的不稳定性
Instability of gravitational and electromagnetic perturbations of extremal Reissner-Nordström spacetime
论文作者
论文摘要
我们研究了极端的引力和电磁扰动的线性稳定性问题，$ | \ Mathcal {q} | = m，$ reissner-nordströmSpacetime，作为Einstein-Maxwell方程的解决方案。我们的工作使用并扩展了Giorgi的框架\ Cite {giorgi2019boundedness，Giorgie2020boundedness}，与次级案例相反，我们证明，沿着活动范围内的一组不变的数量，我们证明不稳定性的结果是不稳定的。特别是，我们沿$ \ Mathcal {h}^+ $渐近地证明了衰减，非衰落和多项式爆炸估计，这取决于我们采用的翻译不变衍生物的数量。结果，我们表明，对于通用的初始数据，阳性和负型的通用Teukolsky系统的解决方案都可以满足稳定性和不稳定性结果。值得一提的是，负旋转溶液明显更加不稳定，而极端的曲率组件$ \usewinlineα$在事件范围$ \ Mathcal $ \ Mathcal {h}^+上均不渐进，这是文献中先前未知的结果。
We study the linear stability problem to gravitational and electromagnetic perturbations of the extremal, $ |\mathcal{Q}|=M, $ Reissner-Nordström spacetime, as a solution to the Einstein-Maxwell equations. Our work uses and extends the framework \cite{giorgi2019boundedness,giorgie2020boundedness} of Giorgi, and contrary to the subextremal case we prove that instability results hold for a set of gauge invariant quantities along the event horizon $ \mathcal{H}^+ $. In particular, we prove decay, non-decay, and polynomial blow-up estimates asymptotically along $ \mathcal{H}^+ $, the exact behavior depending on the number of translation invariant derivatives that we take. As a consequence, we show that for generic initial data, solutions to the generalized Teukolsky system of positive and negative spin satisfy both stability and instability results. It is worth mentioning that the negative spin solutions are significantly more unstable, with the extreme curvature component $ \underlineα $ not decaying asymptotically along the event horizon $ \mathcal{H}^+, $ a result previously unknown in the literature.
