Cosmic censorship in higher dimensions. II.

Mahajan, Ashutosh; Goswami, Rituparno; Joshi, Pankaj S.

doi:10.1103/physrevd.72.024006

Cited by 7 publications

(15 citation statements)

References 26 publications

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“…25 it was shown that the condition that t ah is increasing, which is equivalent to the positivity of the first non-vanishing χ, is not only necessary but also sufficient for the local visibility of the central singularity (see also Refs. [32][33][34]. Furthermore it can be proven that if there is one outgoing radial null geodesic that escapes the singularity then there is necessarily a whole family of such geodesics.…”

Section: Trapped Surfaces and Outgoing Null Geodesicsmentioning

confidence: 99%

Recent Developments in Gravitational Collapse and Spacetime Singularities

Joshi

Malafarina

2011

Int. J. Mod. Phys. D

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233

202

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It is now known that when a massive star collapses under the force of its own gravity, the final fate of such a continual gravitational collapse will be either a black hole or a naked singularity under a wide variety of physically reasonable circumstances within the framework of general theory of relativity. The research of recent years has provided considerable clarity and insight on stellar collapse, black holes and the nature and structure of spacetime singularities. We discuss several of these developments here. There are also important fundamental questions that remain unanswered on the final fate of collapse of a massive matter cloud in gravitation theory, especially on naked singularities which are hypothetical astrophysical objects and on the nature of cosmic censorship hypothesis. These issues have key implications for our understanding on black hole physics today, its astrophysical applications, and for certain basic questions in cosmology and possible quantum theories of gravity. We consider these issues here and summarize recent results and current progress in these directions. The emerging astrophysical and observational perspectives and implications are dicussed, with particular reference to the properties of accretion discs around black holes and naked singularities, which may provide characteristic signatures and could help distinguish these objects.

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Section: Trapped Surfaces and Outgoing Null Geodesicsmentioning

confidence: 99%

Recent Developments in Gravitational Collapse and Spacetime Singularities

Joshi

Malafarina

2011

Int. J. Mod. Phys. D

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233

202

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“…In particular, the class of solutions that we find extend again vanishing radial stress models as dust [4,24]. We will find the complete spectrum of endstates, analyzing if and how it is modified by the dimension of the spacetime N. In particular, naked singularities will be proved to survive in any larger dimension, despite earlier results contained in [10,20] see discussion at the end.…”

Section: Introductionmentioning

confidence: 84%

“…There have been previous works trying to explain the endstate in terms of the kinematical properties of the spacetime, in particular the shear at initial time [10,20].…”

Section: Discussionmentioning

confidence: 99%

“…As one can see, the contribution of the dimension N, when it is larger than four, basically enters in the behavior of the apparent horizon, that behaves like r 1+2/ (N −3) , which is no more an integer power of r as N ≥ 6, and it is always leading upon the "kinematical" contribution of N -i.e. the last term in (20). Since the contribution of √ ∆(r, 0) is always an integer power of r -see below -this fact results in the lack of critical case when N ≥ 6.…”

Section: Naked Singularity Vs Black Hole Formationmentioning

confidence: 99%

“…(ii) vanishing radial stress solutions [20], that occur when Ψ is a function of r only, but Y may also depend on R, (iii) acceleration free solutions, when Y is a function of r only but Ψ may also depend on R (note that the norm of the acceleration is simply given by Y ,R )…”

Section: Examplesmentioning

confidence: 99%

See 2 more Smart Citations

The dimensional dependence of naked singularity formation in spherical gravitational collapse

Giambò¹,

Quintavalle²

2008

Class. Quantum Grav.

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The complete spectrum of the endstates -naked singularities, or blackholes -of gravitational collapse is analyzed for a wide class of N -dimensional spacetimes in spherical symmetry, which includes and generalizes the dust solutions and the case of vanishing radial stresses. The final fate of the collapse is shown to be fully determined by the local behavior of a single scalar function and by the dimension N of the spacetime. In particular, the "critical" behavior of the N = 4 spacetimes, where a sort of phase transition from black hole to naked singularity can occur, is still present if N = 5 but does not occur if N > 5, independently from the initial data of the collapse. Physically, the results turn out to be related to the kinematical properties of the considered solutions.

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Tipler naked singularities in N dimensions

Solanki,

Mosani,

Deshpande

et al. 2024

Class. Quantum Grav.

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A spacetime singularity, identified by the existence of incomplete causal geodesics in the spacetime, is called a (Tipler) strong curvature singularity if the volume form acting on independent Jacobi fields along causal geodesics vanishes in the approach of the singularity. It is called naked if at least one of these causal geodesics is past incomplete. Here, we study the formation of strong curvature naked singularities arising from spherically symmetric gravitational collapse of general type-I matter fields in an arbitrarily finite number of dimensions. In the spirit of Joshi and Dwivedi (1993 Phys. Rev. D 47 5357), and Goswami and Joshi (2007 Phys. Rev. D 76 084026), beginning with regular initial data, we derive two distinct (but not mutually exclusive) conditions, which we call the positive root condition (PRC) and the simple positive root condition (SPRC), that serve as necessary and sufficient conditions, respectively, for the existence of naked singularities. In doing so, we generalize the results of both the aforementioned works. We further restrict the PRC and the SPRC by imposing the curvature growth condition (CGC) of Clarke and Krolak (1985 J. Geom. Phys. 2(2) 127) on all causal curves that satisfy the causal convergence condition. The CGC then gives a sufficient condition ensuring that the naked singularities implying the PRC and implied by the SPRC, are of strong curvature type and hence correspond to the inextendibility of the spacetime. Using the CGC, we extend the results of Mosani et. al. (2020 Phys. Rev. D 101 044052) (that hold for dimension N=4) to the case N=5, showing that strong curvature naked singularities can occur in this case. However, for the case N≥6, we show that past-incomplete causal curves that identify naked singularities do not satisfy the CGC. These results shed light on the validity of the cosmic censorship conjectures in arbitrary dimensions.

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Cosmic censorship in higher dimensions. II.

Cited by 7 publications

References 26 publications

Recent Developments in Gravitational Collapse and Spacetime Singularities

Recent Developments in Gravitational Collapse and Spacetime Singularities

The dimensional dependence of naked singularity formation in spherical gravitational collapse

Tipler naked singularities in N dimensions

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