Naked singularity formation in generalized Vaidya space-time

Abstract

The gravitational collapse in generalized Vaidya space-time is considered. It is known that the end state of gravitational collapse, as to whether a black hole or a naked singularity is formed, depends on the mass function M (v, r). Here we give conditions for the mass function which correspond to the equation of the state P = αρ. where α ∈ (0, 1/3], and according to these conditions we obtain either a black hole or a naked singularity as the end state of gravitational collapse. We also give the conditions for the mass function under which the singularity is gravitationally strong. We present simple examples showing when the result of gravitational collapse is a naked singularity and when this singularity is strong.

The Negative Energy in Generalized Vaidya Spacetime

“…The properties of generalized Vaidya spacetime has been studied for the equation of the state P = αρ where α belongs to the interval [0 , 1] in articles [8,9]. If we satisfy this equation of the state then the mass function M(r, v) has the form…”

“…M. Mkenyley et al investigated the question about the gravitational collapse of generalized Vaidya spacetime [7] and showed that the result of this collapse might be the naked singularity. Furthermore, the conditions for the mass function were obtained [8,9]. Vaidya spacetime is the one of the earliest examples of cosmic censorship conjecture violation [10].…”

Some remarks on the naked singularity phenomenon

“…This paper considers gravitational collapse of thin radiating shells (Vertogradov 2016). The first shell collapses at the central singularity at r = υ = 0 where M(0, 0) = 0.…”

“…Let us consider the simplest case, when the equation of the state is ) are the same (Vertogradov 2016).…”

“…The EMT must be physically relevant and must satisfy energy conditions: weak, strong and dominant ones (Hawking, Ellis 1973). Nowadays there are a lot of gravitational collapse models which result in naked singularities (Goswami, Joshi 2007;Vertogradov 2016;2018;Mkenyeley, Goswami, Maharaj 2014); however, if the EMT satisfies all necessary energy conditions, these naked singularities are temporary. Nevertheless, one en-V. D. Vertogradov ergy condition-the strong one-can be violated.…”