Vaidya Collapse with Nonzero Radial Pressure and Charge

Aroonkumar Beesham

doi:10.3390/axioms9020052

Abstract

The cosmic censorship hypothesis is regarded as one of the most important unsolved problems in classical general relativity; viz., will generic gravitational collapse of a star after it has exhausted its nuclear fuel lead to black holes only, under reasonable physical conditions. We discuss the collapse of a fluid with nonzero radial pressure within the context of the Vaidya spacetime considering a decaying cosmological parameter as well as nonzero charge. Previously, a similar analysis was done, but without considering charge. A decaying cosmological parameter may also be associated with dark energy. We found that both black holes and naked singularities can form, depending upon the initial conditions. Hence, charge does not restore the validity of the hypothesis. This provides another example of the violation of the cosmic censorship hypothesis. We also discuss some radiating rotating solutions, arriving at the same conclusion.

Highlights

The cosmic censorship hypothesis (CCH) [1] is regarded as one of the most important unsolved problems in classical general relativity theory
If we look at a typical star and ask what happens after it has exhausted its nuclear fuel, there are three possibilities, depending upon the mass of the star
We studied the collapse of this spacetime and found that naked singularities or black holes could form, depending upon the initial conditions [13]

Summary

Introduction

The cosmic censorship hypothesis (CCH) [1] is regarded as one of the most important unsolved problems in classical general relativity theory. The question that arises is whether the introduction of pressure can help to avoid the naked singularity and restore the validity of the cosmic censorship hypothesis. An interesting generalization of the Vaidya spacetime has been given [7] which incorporates nonzero radial pressure: 2m(v) Λ(v)r2. We studied the collapse of this spacetime and found that naked singularities or black holes could form, depending upon the initial conditions [13]. The gravitational collapse of the Vaidya model is studied with a variable cosmological parameter and nonzero charge, to see whether the hypothesis is still violated. One can ask the obvious question as to whether charged stars exist in nature, since we expect stars to be electrically neutral. In a physically realistic star, we expect rotation, and we investigate some rotating stars to see whether charge can affect the outcome of the collapse

Nonzero Charge in Vaidya

Radiating Rotating Stars

Discussion

Conclusions