In this paper the structure of the generalized Vaidya spacetime when the
type-II of the matter field satisfies the equation of the state $P=\rho$ is
investigated. Satisfying all energy conditions we show that this spacetime
contains the ‘eternal’ naked singularity. It means that once the singularity is
formed it will never be covered with the apparent horizon. However, in the case
of the apparent horizon formation the resulting object is a white hole. We also
prove that this spacetime contains only null naked singularity.

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