On Timelike Naked Singularities associated with Noncompact Matter Sources

We show the existence of timelike naked singularities which are not hidden by a horizon and which are associated to spherically symmetric (noncompact) matter sources extending from r = 0 to r = ∞. Our asymptotically flat solutions do represent observable timelike naked singularities where the scalar curvature R and volume mass density ρ(r) are both singular at r = 0. To finalize we explain the Finsler geometric origins behind the matter field configuration obeying the weak energy conditions and that leads to a timelike naked singularity. Long ago Penrose [1] proposed the Cosmic Censorship Conjecture (CCC) stating that singularities which form in a gravitational collapse and consistent with Einstein’s [2] field equations should never be visible to an outside observer or they should be hidden inside a horizon. Recently, Deshingkar [3] studied singularities which can form in a spherically symmetric gravitational collapse of a general matter field obeying the weak energy condition. He showed that no energy can reach an outside observer from a null naked singularity. That means they will not be a serious threat to the Cosmic Censorship Conjecture (CCC). For timelike naked singularities, where only the central shell gets singular, the redshift is always finite and they can in principle, carry energy to a faraway observer. Hence for proving or disproving CCC the study of timelike naked singularities is more important. The results of [3] were very general and independent of the initial data and the form of the matter. The purpose of this letter is to show the existence of timelike naked singularities which are not hidden by a horizon and which are associated to spherically symmetric noncompact matter sources extending for r = 0 to r = ∞. Our asymptotically flat solutions do represent observable timelike naked singularities where the scalar curvature R and volume mass density ρ(r) are both singular at r = 0 while the metric remains finite at r = 0. The Einstein