10^20 eV Cosmic-Ray and Particle Physics with Kilometer-Scale Neutrino Telelscopes

We show that a kilometer-scale neutrino observatory, though optimized for TeV to PeV energy, is sensitive to the neutrinos associated with super-EeV sources. These include super-heavy relics, neutrinos associated with the Greisen cutoff, and topological defects which are remnant cosmic structures associated with phase transitions in grand unified gauge theories. It is a misconception that new instruments optimized to EeV energy are required to do this important science. Because kilometer-scale neutrino telescopes can reject atmospheric backgrounds by establishing the very high energy of the signal events, they have sensitivity over the full solid angle, including the horizon where most of the signal is concentrated. This is important because up-going neutrino-induced muons, routinely considered in previous calculations, are absorbed by the Earth.