Symmetry and instability of marginally outer trapped surfaces

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.

Symmetry and instability of marginally outer trapped surfaces Articles