Conditions for the occurence of strong curvature singularities

Clarke, C. J. S.; Królak, A.

doi:10.1016/0393-0440(85)90012-9

Cited by 206 publications

(246 citation statements)

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“…We have extended this study to higher dimensional Vaidya metric, and found that strong curvature naked singularities do arise for slightly higher value of inhomogeneity parameter. We have checked, for naked singularities to be gravitationally strong, by method in [15] and by alternative approach proposed by Nolan [16] as well, and both seem to be in agreement. It is straight forward to extend…”

supporting

confidence: 61%

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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supporting

confidence: 61%

Higher dimensional radiation collapse and cosmic censorship

Ghosh¹,

Saraykar

2000

Phys. Rev. D

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“…The Cauchy horizon singularity is weak, if R is twice-integrable. (This last statement can be made precise [11].) For positive value of n this is indeed the case.…”

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confidence: 83%

Survival of the black hole’s Cauchy horizon under noncompact perturbations

Burko

2002

Phys. Rev. D

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We study numerically the evolution of spactime, and in particular of a spacetime singularity, inside a black hole under a class of perturbations of non-compact support. We use a very simplified toy model of a spherical charged black hole which is perturbed nonlinearly by a self-gravitating, spherical scalar field. The latter grows logarithmically with advanced time along an outgoing characteristic hypersurface. We find that for that class of perturbations a portion of the Cauchy horizon survives as a non-central, null singularity.

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“…According to [21], a lightlike geodesic meets a strong singularity, according to Tipler's definition, at proper time τ 0 if and only if the integral of the Ricci tensor…”

Section: Strength Of Singularities Along Lightlike Geodesicsmentioning

confidence: 99%

“…And the same happens with models with η 0 = 1, k = −1, c 0 = 1, though those with η 1 ∈ (1, 3) have also strong singularities according to Królak. Since the condition on integrals of the Ricci tensor is not also a necessary condition for the appearance of strong singularities, we have to check other ways to get information about the η 0 = 0 and η 0 = 1 models. For Tipler's definition [21], if a causal geodesic with velocity u meets a strong singularity, then the integral…”

Section: Strength Of Singularities Along Timelike Geodesicsmentioning

confidence: 99%

Classification of cosmological milestones

2006

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In this paper causal geodesic completeness of FLRW cosmological models is analysed in terms of generalised power expansions of the scale factor in coordinate time. The strength of the found singularities is discussed following the usual definitions due to Tipler and Królak. It is shown that while classical cosmological models are both timelike and lightlike geodesically incomplete, certain observationally alllowed models which have been proposed recently are lightlike geodesically complete.

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Conditions for the occurence of strong curvature singularities

Cited by 206 publications

References 6 publications

Higher dimensional radiation collapse and cosmic censorship

Higher dimensional radiation collapse and cosmic censorship

Survival of the black hole’s Cauchy horizon under noncompact perturbations

Classification of cosmological milestones

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