The structure of the generalized Vaidya spacetime containing the eternal naked singularity

TL;DR

This paper investigates the structure of a generalized Vaidya spacetime with a specific matter field, revealing the presence of an eternal naked singularity that remains uncovered and is characterized as a null naked singularity.

Contribution

It demonstrates that under certain conditions, the generalized Vaidya spacetime contains an eternal null naked singularity that never gets covered by an apparent horizon.

Findings

Contains an eternal naked singularity that remains uncovered.

The singularity is characterized as a null naked singularity.

In cases with apparent horizon formation, the object is a white hole.

Abstract

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.