  This paper explores a complete representation of the Vaidya model, a radial
flux of radiation in the eikonal approximation, used for modeling various
phenomena in both classical and semi-classical General Relativity and
Astrophysics. The majority of the applications of the Vaidya model have been
formulated in an incomplete representation. A complete representation is
obtained here by direct integration of the Einstein field equations. We present
the methodology to obtain this complete representation, and its utility in the
modeling of general relativistic phenomena.
