极值Reissner-Nordström时空的非线性标量扰动
Nonlinear scalar perturbations of extremal Reissner-Nordström spacetimes
摘要：
我们提出了第一个严格的研究极端黑洞时空的非线性波动方程没有任何对称性假设的解决方案。具体地说，我们证明了非线性波动方程的解的整体存在性与渐近爆破满足零条件的极值Reissner-Nordström背景。这一结果表明，极值视界不稳定性在模型非线性理论中仍然存在。我们的证明关键依赖于一个新的向量场的方法，使我们能够获得几乎尖锐的衰减估计。
英文摘要：
We present the first rigorous study of nonlinear wave equations on extremal black hole spacetimes without any symmetry assumptions on the solution. Specifically, we prove global existence with asymptotic blow-up for solutions to nonlinear wave equations satisfying the null condition on extremal Reissner-Nordström backgrounds. This result shows that the extremal horizon instability persists in model nonlinear theories. Our proof crucially relies on a new vector field method that allows us to obtain almost sharp decay estimates.
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