Symmetry and instability of marginally outer trapped surfaces
arXiv:2311.02063 · doi:10.1088/1361-6382/ad3dab
Abstract
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.
17 pages, 2 figures. Additional references added in v2
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