We consider smooth solutions of the wave equation, on a fixed black hole region of a subextremal Reissner–Nordström (asymptotically flat, de Sitter or anti-de Sitter) spacetime, whose restrictions to the event horizon have compact support. We provide criteria, in terms of surface gravities, for the waves to remain in \(C^l\), \(l\geqslant 1\), up to and including the Cauchy horizon. We also provide sufficient conditions for the blow up of solutions in \(C^1\) and \(H^1\).

中文翻译：

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Reissner–Nordström柯西视界的高阶线性稳定性和不稳定性

我们考虑在极下的Reissner–Nordström（渐近平坦，de Sitter或anti-de Sitter）时空的固定黑洞区域上波动方程的光滑解，其对事件视界的限制具有紧凑的支持。根据表面重力，我们提供了波保持在（C ^ l \），\（l \ geqslant 1 \）内，直至并包括柯西地平线的标准。我们还为\（C ^ 1 \）和\（H ^ 1 \）中的解爆炸提供了充分的条件。