The structure of the generalized Vaidya space–time containing the eternal naked singularity

Abstract

In this paper, the structure of the generalized Vaidya space–time when the type-II of the matter field satisfies the equation of the state [Formula: see text] is investigated. Satisfying all energy conditions, we show that this space–time 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 space–time contains only null naked singularity.