The eternal naked singularity formation in the case of gravitational collapse of generalized Vaydia spacetime

TL;DR

This paper investigates gravitational collapse in generalized Vaidya spacetime, revealing conditions under which naked singularities form and persist, challenging the cosmic censorship hypothesis.

Contribution

It demonstrates that under certain matter conditions, gravitational collapse leads to eternal naked singularities, with the apparent horizon either not forming or disappearing quickly.

Findings

Dust collapse results in no apparent horizon and a naked singularity.

Negative pressure can cause the formation of an eternal naked singularity.

Apparent horizon appears and then quickly disappears in negative pressure cases.

Abstract

In this paper, we consider the gravitational collapse of generalized Vaidya space-time when the matter satisfies the equation of the state either $P=0$ or $P=-\alpha \rho$, where $0 < \alpha < 1$. We show that in the case when type I of matter field is dust, then the apparent horizon will never appear, but there is now a family of null radial future-directed geodesics which terminated at the central singularity in the past. Also, we show that in the case of negative pressure, the result of the gravitational collapse might be the naked singularity and the apparent horizon appears and in very short time disappears again. In the case of the negative pressure, we show that the result of the gravitational collapse might be the eternal naked singularity.