We present a new model for the source XBT 1730 - 335, the rapid burster. The model is based on the idea that radiation plays an important role in transporting angular momentum from relativistic accretion disks an idea which is fully justified by direct calculation of the radiation torques. The calculations we utilize are fully relativistic and cast in a Kerr geometry; they describe the evolution of a geometrically thin, axisymmetric, irradiated accretion disk around a nonmagnetic neutron star.We calculate not only temporal, but also spectral properties, and we address many of the significant features of the real system, including the burst-energy/waiting time relationship, the unique nature of this object, the source spectrum, the outburst cycle, the nonbursting state, and the unusual type 1 burst properties which are sometimes observed. By comparing the results of our calculations with the observed properties we deduce a great deal about the nature of this object: the rapid burster is a non-magnetic, "critically compact," slowly rotating neutron star in a highly eccentric binary system with a period of 6 months; accretion proceeds via a massive, nearly dissipationless disk which is at an inclination of about 50° to the line of sight. Overall the model is very successful, although one clear predictive failure is noted. An important feature is that determination of success or failure of the model is not contingent on understanding the local dissipative processes acting in the accretion flow.