In this talk, we will see the potentially non-trivial dynamics of elementary particles on so-called Carroll geometries when restricted to a 2+1 dimensional plane. Such geometries are crucial in General Relativity as they are featured on important physical structures, such as black hole horizons, conformal null infinity, or even some hypersurfaces inside gravitational waves. The distinct behavior of the planar case is due to the presence of two non-trivial central extensions of the Carroll algebra, which means that associated elementary particles feature two additional (effective) physical parameters. We will show that these parameters lead to non-trivial effects when particles are coupled to an external electromagnetic field, and explicitly work out the implications for Kerr-Newmann horizon.
