Physical nature of the central singularity in spherical collapse

It was recently shown that the metric functions which describe a spherically symmetric spacetime with vanishing radial pressure can be explicitly integrated. We investigate the nakedness and curvature strength of the shell-focusing singularity in that space-time. If the singularity is naked, the relation between the circumferential radius and the Misner-Sharp mass is given by R ≈ 2y0m β with 1/3 < β ≤ 1 along the first radial null geodesic from the singularity. The β is closely related to the curvature strength of the naked singularity. For example, for the outgoing or ingoing null geodesic, if the strong curvature condition (SCC) by Tipler holds, then β must be equal to 1. We define the "gravity dominance condition" (GDC) for a geodesic. If GDC is satisfied for the null geodesic, both SCC and the limiting focusing condition (LFC) by Królak hold for β = 1 and y0 = 1, not SCC but only LFC holds for 1/2 ≤ β < 1, and neither holds for 1/3 < β < 1/2, for the null geodesic. On the other hand, if GDC is satisfied for the timelike geodesic r = 0, both SCC and LFC are satisfied for the timelike geodesic, irrespective of the value of β. Several examples are also discussed.

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“…This fact was already shown by Deshingkar, Joshi and Dwivedi (1999). This can be confirmed by the result of Sec.…”

Section: Examples a Dust Collapsesupporting

confidence: 81%

“…It is important that the strength of the singularity is determined by the curvature divergence not only on the null geodesic but also on the timelike geodesic. Recently, Deshingkar, Joshi and Dwivedi (1999) showed that both SCC and LFC are satisfied for the timelike geodesics which terminate at the shell-focusing singularity.…”

Section: Introductionmentioning

confidence: 99%

Nakedness and curvature strength of a shell-focusing singularity in spherically symmetric spacetime with vanishing radial pressure

Harada

Nakao

Iguchi

1999

Class. Quantum Grav.

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“…The singularity satisfies not the strong curvature condition (SCC) defined by Tipler [32] but only the limiting focusing condition (LFC) defined by Królak [33] for radial null geodesics which terminate at the singularity. On the other hand, the singularity satisfies both LFC and SCC for radial timelike geodesics [21].…”

Section: Lemaître-tolman-bondi Solutionmentioning

confidence: 99%

“…For the C ∞ case, the redshift is finite and the naked singularity is not very strong. See [21][22][23] for details. Though the Einstein equation does not require such strong differentiability to initial data, we usually set such initial data in most astrophysical numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

Power, energy, and spectrum of a naked singularity explosion

2000

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It is well known that a naked singularity occurs in the gravitational collapse of an inhomogeneous dust ball from an initial density profile which is physically reasonable. In this paper we show that explosive radiation is emitted during the formation process of the naked singularity while we fix the background spacetime. The energy flux is proportional to (tCH − t) −3/2 for a minimally coupled massless scalar field, while it is proportional to (tCH − t) −1 for a conformally coupled massless scalar field, where tCH − t is the "remaineing time" until the distant observer could observe the singularity if the naked singularity was formed. As a consequence, the radiated energy grows unboundedly for both scalar fields. The amount of the power and energy depends on the parameters which characterize the initial density profile but do not depend on the gravitational mass of the cloud. In particular, there is a characteristic frequency νs of the singularity above which the divergent energy is radiated. The energy flux is dominated by particles of which the wavelength is about tCH − t at each moment. The observed total spectrum is nonthermal, i.e., νdN/dν ∼ (ν/νs) −1 for ν > νs. If the naked singularity formation could continue until a considerable fraction of the total energy of the dust cloud is radiated, the radiated energy would reach about 10 54 (M/M⊙)erg. The calculations are based on the geometrical optics approximation which turns out to be consistent for a rough order estimate. The analysis does not depend on whether or not the naked singularity occurs in its exact meaning. This phenomenon may provide a new candidate for a source of ultrahigh energy cosmic rays or a central engine of γ-ray bursts.

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“…The strength of singularity is an important issue because there have been attempts to relate it to stability [14]. A singularity is termed gravitationally strong or simply strong, if it destroys by crushing or stretching any object which falls in to it.…”

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confidence: 99%

Higher dimensional radiation collapse and cosmic censorship

Ghosh¹,

Saraykar

2000

Phys. Rev. D

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We study the occurrence of naked singularities in the spherically symmetric collapse of radiation shells in a higher dimensional spacetime. The necessary conditions for the formation of a naked singularity or a black hole are obtained. The naked singularities are found to be strong in the Tipler's sense and thus violating cosmic censorship conjecture.PACS numbers: 04.20.DwThe cosmic censorship conjecture (CCC) put forward some three decades ago by Penrose [1] says that in generic situation all singularities arising from regular initial data are clothed by event horizon. Since CCC remains as an unresolved issue in classical general relativity, examples which appear to violate conjecture remain important and may be valuable when one attempts to formulate notion of CCC in concrete mathematical form. The Vaidya solution [2] is most commonly used as a testing ground for various forms of the CCC. In particular, Papapetrou [3] first showed that this solution can give rise to the formation of naked singularities and thus provided one of the earlier counter examples to CCC. Since then, the solution is extensively studied in gravitational collapse with reference to CCC (see e.g. [4] and references therein). Lately, there has been interest in studying gravitational collapse in higher dimensions [5]. This brief report searches for the occurrence of naked singularities in higher dimensional Vaidya spacetime and if they do, to investigate whether the dimensionality of spacetime has any role in the nature of singularities. We find that higher dimensional Vaidya spacetime admit strong-curvature naked singularities in the Tipler's [6] sense.The idea that spacetime should be extended from four to higher dimensions was introduced by Kaluza and Klein [7] to unify gravity and electromagnetism. Five dimensional (5D) spacetime is particularly more relevant because both 10D and 11D super-gravity theories yield solutions where a 5D spacetime results after dimensional reduction [8]. Hence, we shall confine ourselves to 5D case. It should be noted that higher dimensional spacetimes where all dimensions are in the equal foot, like ones to be considered here, are not so realistic, as we are living in effectively 4-dimensional spacetime. So in principle one might expect that by dimensional reduction the higher dimensional spacetime should reduce to our 4-dimensional world. In this sense, the models considered in this paper are ideal. * Electronic address: sgghosh@yahoo.com † Electronic address: sarayaka@nagpur.dot.net.inThe metric of collapsing Vaidya models in 5D case is [9]where v is null coordinate which represents advanced Eddington time with −∞ < v < ∞, r is radial coordinate with 0 ≤ r < ∞, dΩ 2 = dθ 2 1 + sin 2 θ 1 (dθ 2 2 + sin 2 θ 2 dθ 2 3 ) is a metric of 3 sphere and the arbitrary function m(v) (which is restricted only by the energy conditions), represents the mass at advanced time v. The energy momentum tensor can be written in the formwith the null vector k a satisfying k a = −δ v a and k a k a = 0. We have used the units whi...

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Physical nature of the central singularity in spherical collapse

Cited by 52 publications

References 17 publications

Nakedness and curvature strength of a shell-focusing singularity in spherically symmetric spacetime with vanishing radial pressure

Nakedness and curvature strength of a shell-focusing singularity in spherically symmetric spacetime with vanishing radial pressure

Power, energy, and spectrum of a naked singularity explosion

Higher dimensional radiation collapse and cosmic censorship

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