  Finite-energy particles in free fall can collide with diverging
center-of-mass energy near rapidly rotating black holes. What are the most
salient observational signatures of this remarkable geometric effect? Here we
revisit the problem from the standpoint of the near-horizon extreme Kerr
geometry, where these collisions naturally take place. It is shown that the
ingoing particle kinematics admits a simple, universal form. Given a scattering
cross section, determination of emission properties is reduced to evaluation of
particular integrals on the sky of a near-horizon orbiting particle. We
subsequently apply this scheme to the example of single-photon bremsstrahlung,
substantiating past results which indicate that ejected particles are
observable, but their energies are bounded by the rest masses of the colliding
particles. Our framework is readily applicable for any scattering process.
