It is customary to consider only light sources, or sources moving with a velocity v lower than the velocity of light in vacuum (c). It is assumed in this connection that the Vavilov-Cerenkov effect and the anomalous Doppler effect are possible only in media and waves for which the refractive index n(ω) > 1. For this reason, the phase velocity of the waves is cph = [c/n(ω)] cph. Yet, as is well known, there exist also sources, with velocity v > c. Examples are light spots produced on a remote screen by a rotating source of light or particles. The spot velocity is v = ΩR, where Ω is the angular velocity of source rotation and R is the distance to the screen. The condition v > c can be realized on the Earth, and is practically always realized under astronomical conditions for pulsar radiation. It is emphasized in the article that superluminal sources are equivalent in a wide range to subluminal ones, and, concretely, can generate Cerenkov radiation in vacuum and in a medium with n(ω) < 1. The article considers several corresponding possibilities. From this point of view of radiation theory, a major difference between the superluminal and subluminal sources is that the former can not be individual particles (electrons, protons, etc.), since their velocity is always smaller than c. Superluminal sources, which must thus consist of aggregates of particles, must thus have nonzero dimensions, and this leads to a corresponding formation of a spectrum of the radiated frequencies on the short-wave side. Regardless of whether superluminal sources will find interesting applications in physics and astronomy, a study of the radiation of superluminal sources of electromagnetic and gravitational waves (and possibly also neutrinos) is in the authors' opinion of undisputed physical interest.
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