  General relativity predicts that the Kerr black hole develops qualitatively
new and surprising features in the limit of maximal spin. Most strikingly, the
region of spacetime near the event horizon stretches into an infinitely long
throat and displays an emergent conformal symmetry. Understanding dynamics in
this NHEK (Near-Horizon Extreme Kerr) geometry is necessary for connecting
theory to upcoming astronomical observations of high-spin black holes. We
review essential properties of NHEK and its relationship to the rapidly
rotating Kerr black hole. We then completely solve the geodesic equation in the
NHEK region and describe how the resulting trajectories transform under the
action of its enhanced symmetries. In the process, we derive explicit
expressions for the angular integrals appearing in the Kerr geodesic equation
and obtain a useful formula, valid at arbitrary spin, for a particle's polar
angle in terms of its radial motion. These results will aid in the analytic
computation of astrophysical observables relevant to ongoing and future
experiments.
