Marginally outer trapped surfaces in the Schwarzschild spacetime: Multiple self-intersections and extreme mass ratio mergers

We study the open and closed axisymmetric marginally outer trapped surfaces contained in leaves of constant Painlev\'e-Gullstrand time for Schwarzschild spacetimes. We identify a family of closed marginally outer trapped surface (MOTS) in the black hole interior characterized by an arbitrary number of self-intersections. This suggests that the self-intersecting behavior reported by Pook-Kolb et al. [Phys. Rev. D 100, 084044 (2019)] may be a far more generic phenomenon than expected. We also consider open surfaces, finding that their behavior is highly constrained but includes surfaces with multiple self-intersections inside the horizon. We argue that the behavior of open MOTS identifies and constrains the possible local behavior of MOTS during extreme mass ratio mergers.