Cosmic censorship violation in non-self-similar Tolman-Bondi models

Dwivedi, I. H.; Joshi, Pankaj S.

doi:10.1088/0264-9381/9/7/001

Cited by 69 publications

(61 citation statements)

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“…One should note that departure from the homogeneous models by way of introducing arbitrarily small inhomogeneity does not necessarily make the singularity naked, as pointed out by our calculations here. This agrees with the earlier results such as those in [3,5,6].…”

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confidence: 94%

“…An important subcase which could be examined in this context is the spherically symmetric but inhomogeneous distribution of dust which collapses under the force of gravity. The general solutions to Einstein equations for this case have been given by the Tolman-Bondi spacetimes [2], and it has been demonstrated that naked singularities can occur as the end state of such a collapse [3,4,5,6]. In particular, it was pointed out in [5,6] that the collapse ends in a naked singularity or a black hole depending on whether or not a certain algebraic equation involving the metric functions and their derivatives has positive real roots.…”

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confidence: 99%

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Role of initial data in the gravitational collapse of inhomogeneous dust

Joshi

Singh

1995

Phys. Rev. D

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We consider here the gravitational collapse of a spherically symmetric inhomogeneous dust cloud described by the Tolman-Bondi models. By studying a general class of these models, we find that the end state of the collapse is either a black hole or a naked singularity, depending on the parameters of the initial density distribution, which are ρ c , the initial central density of the massive body, and R 0 , the initial boundary. The collapse ends in a black hole if the dimensionless quantity β constructed out of this initial data is greater than 0.0113, and it ends in a naked singularity if β is less than this number. A simple interpretation of this result can be given in terms of the strength of the gravitational potential at the starting epoch of the collapse.

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confidence: 94%

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confidence: 99%

Role of initial data in the gravitational collapse of inhomogeneous dust

Joshi

Singh

1995

Phys. Rev. D

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“…Within this context, several gravitational collapse settings have been investigated over the past years which represent the occurrence of naked singularities. 3 Work along this line has been reported in the literature within a variety of models; among them we quote the role of inhomogeneities within the matter distribution on the final fate of gravitational collapse [12][13][14][15][16][17][18][19][20][21][22], collapse of a perfect fluid with heat conduction [23][24][25][26], the effects of shear on the collapse end-product [27][28][29][30], and the collapse process in the context of different gravitational theories [31,32] (see also [33,34] for recent reviews).…”

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confidence: 99%

Collapse and dispersal of a homogeneous spin fluid in Einstein–Cartan theory

2015

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In the present work, we revisit the process of gravitational collapse of a spherically symmetric homogeneous dust fluid which is described by the OppenheimerSnyder (OS) model (Oppenheimer and Snyder in Phys Rev D 56:455, 1939). We show that such a scenario would not end in a spacetime singularity when the spin degrees of freedom of fermionic particles within the collapsing cloud are taken into account. To this purpose, we take the matter content of the stellar object as a homogeneous Weyssenhoff fluid. Employing the homogeneous and isotropic FLRW metric for the interior spacetime setup, it is shown that the spin of matter, in the context of a negative pressure, acts against the pull of gravity and decelerates the dynamical evolution of the collapse in its later stages. Our results show a picture of gravitational collapse in which the collapse process halts at a finite radius, whose value depends on the initial configuration. We thus show that the spacetime singularity that occurs in the OS model is replaced by a non-singular bounce beyond which the collapsing cloud re-expands to infinity. Depending on the model parameters, one can find a minimum value for the boundary of the collapsing cloud or correspondingly a threshold value for the mass content below which the horizon formation can be avoided. Our results are supported by a thorough numerical analysis.

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“…They have interestingly shown that for marginally bound case naked singularity is possible only upto five dimension while naked singularity may be possible in all dimensions for non marginally bound case. Then Goswami and Joshi [13] have pointed out that this peculiar feature of naked singularity (in marginal bound case) is due to the choice of the initial condition.In the present paper we study gravitational collapse for non-marginally bound case considering non self-similar solutions and it is generalization to higher dimension of the Dwivedi and Joshi [14]. The geodesic equations can not completely solved due to the presence of the complicated hypergeometric function.…”

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confidence: 99%

“…In the present paper we study gravitational collapse for non-marginally bound case considering non self-similar solutions and it is generalization to higher dimension of the Dwivedi and Joshi [14]. The geodesic equations can not completely solved due to the presence of the complicated hypergeometric function.…”

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The Study of Gravitational Collapse Model in Higher Dimensional Spacetime

Debnath

Chakraborty

2003

Mod. Phys. Lett. A

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We investigate the end state of the gravitational collapse of an inhomogeneous dust cloud in higher dimensional space-time. The naked singularities are shown to be developing as the final outcome of non-marginally bound collapse. The naked singularities are found to be gravitationally strong in the sense of Tipler .PACS numbers: 04.20.DwThe gravitation collapse is an important and challenging issue in Einstein gravity, especially after the formation of famous singularity theorems [1] and Cosmic Censorship Conjecture (CCC) [2]. Also from the point of view of black hole physics and its astrophysical implications, it is interesting to know the final fate of gravitational collapse [3] in the background of general relativity. The singularity theorems as such can not predict about the visibility of the singularity to an external observer as well as their strength. On the other hand, the CCC is incomplete [4,5] in the sense that there is no formal proof of it as well as there are counter examples of it. However, it has been pointed out recently [6] that the nature of the central shell focusing singularity depends on the choice of the initial data. [12] have studied gravitational collapse in higher dimensional Tolman-Bondi model for both marginally bound and non marginally bound cases. They have interestingly shown that for marginally bound case naked singularity is possible only upto five dimension while naked singularity may be possible in all dimensions for non marginally bound case. Then Goswami and Joshi [13] have pointed out that this peculiar feature of naked singularity (in marginal bound case) is due to the choice of the initial condition.In the present paper we study gravitational collapse for non-marginally bound case considering non self-similar solutions and it is generalization to higher dimension of the Dwivedi and Joshi [14]. The geodesic equations can not completely solved due to the presence of the complicated hypergeometric function. So we present numerical results which favour the formation of naked singularity in any dimension.The n dimensional Tolman-Bondi metric in co-moving co-ordinates is given bywhere ν, λ, R are functions of the radial co-ordinate r and time t and dΩ 2 n−2 represents the metric on the (n − 2)-sphere. Since we assume the matter in the form of dust, the motion of particles will be geodesic allowing us to write e ν = 1. Now from the Einstein's field equations for the metric (1), one can obtain * Electronic address: ujjaldebnath@yahoo.com † Electronic address: subenoyc@yahoo.co.in

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Cosmic censorship violation in non-self-similar Tolman-Bondi models

Abstract: The occurrence of naked singularities in a class of non-self-similar Tolman-Bondi inhomogeneous dust collapse models is pointed out. These are shown to be strong curvature singularities.

Cited by 69 publications

References 10 publications

Role of initial data in the gravitational collapse of inhomogeneous dust

Role of initial data in the gravitational collapse of inhomogeneous dust

Collapse and dispersal of a homogeneous spin fluid in Einstein–Cartan theory

The Study of Gravitational Collapse Model in Higher Dimensional Spacetime

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