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The differential equation governing the time evolution of the self-similar scalar soliton star models, recently proposed by Di Prisco, Herrera, and Esculpi, is studied in detail. All physical plausible modes of evolution are exhibited and compared with the specific solutions presented by Di Prisco, Herrera, and Esculpi

We consider the linear four-momentum radiated by a system of two point charges during two proper-time infinitesimal intervals. As a simple generalization of Schild's result for a single charge, we show that the radiation rate is independent of the hypersurface which is used to integrate Maxwell's tensor and we give an exact covariant expression for it. Using the preceding result we give, in the framework of predictive relativistic mechanics, a definition of radiated linear four-momentum for a system of two interacting charges. We calculate this quantity at the lowest approximation in perturbation theory and we compare our result to the familiar one obtained in the framework of the slow-motion approximation.