The role of trapping in black hole spacetimes In the here presented work we discuss a series of results that are all in one way or another connected to the phenomenon of trapping in black hole spacetimes. First we present a comprehensive review of the Kerr Newman Taub NUT de Sitter family of black hole spacetimes and their most important properties. From there we go into a detailed analysis of the bahaviour of null geodesics in the exterior region of a sub extremal Kerr spacetime. We show that most well known fundamental properties of null geodesics can be represented in one plot. In particular one can see immediately that the ergoregion and trapping are separated in phase space. We then consider the sets of future past trapped null geodesics in the exterior region of a sub extremal Kerr Newman Taub NUT spacetime. We show that from the point of view of any timelike observer outside of such a black hole trapping can be understood as two smooth sets of spacelike directions on the celestial sphere of the observer. Therefore the topological structure of the trapped set on the …