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This paper explores a complete representation of the Vaidya model, a radialflux of radiation in the eikonal approximation, used for modeling variousphenomena in both classical and semi-classical General Relativity andAstrophysics. The majority of the applications of the Vaidya model have beenformulated in an incomplete representation. A complete representation isobtained here by direct integration of the Einstein field equations. We presentthe methodology to obtain this complete representation, and its utility in themodeling of general relativistic phenomena.

Constructing Maximal Extensions of the Vaidya Metric in Israel Coordinates: I. Integration of the Field Equations