We consider an initial data set having a continuous symmetry and a marginally outer trapped surface (MOTS) that is not preserved by this symmetry. We show that such a MOTS is unstable except in an exceptional case. In non-rotating cases we provide a Courant-type lower bound on the number of unstable eigenvalues. These results are then used to prove the instability of a large class of exotic MOTSs that were recently observed in the Schwarzschild spacetime. We also discuss the implications for the apparent horizon in data sets with translational symmetry.

中文翻译：

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边缘外俘获表面的对称性和不稳定性

我们考虑具有连续对称性和不被这种对称性保留的边缘外陷表面（MOTS）的初始数据集。我们证明，除了特殊情况外，这样的 MOTS 是不稳定的。在非旋转情况下，我们提供不稳定特征值数量的库朗型下界。这些结果随后被用来证明最近在史瓦西时空中观察到的一大类奇异 MOTS 的不稳定性。我们还讨论了具有平移对称性的数据集中表观地平线的含义。