Exotic marginally outer trapped surfaces in rotating spacetimes of any dimension

The recently developed MOTSodesic method for locating marginally outer trapped surfaces (MOTSs) was effectively restricted to non-rotating spacetimes. In this paper we extend the method to include (multi-)axisymmetric time slices of (multi-)axisymmetric spacetimes of any dimension. We then apply this method to study MOTSs in the BTZ, Kerr and Myers–Perry black holes. While there are many similarities between the MOTSs observed in these spacetimes and those seen in Schwarzschild and Reissner-Nordström, details of the more complicated geometries also introduce some new, previously unseen, behaviours.