Shell crossing in generalized Tolman-Bondi spacetimes

Gonçalves, Sérgio M. C. V.

doi:10.1103/physrevd.63.124017

Cited by 23 publications

(32 citation statements)

References 18 publications

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“…Moreover, according to the strong version of the CCC, such singularities are * Electronic address: sgghosh@iucaa.ernet.in not even locally naked, i.e., no non-spacelike curve can emerge from such singularities (see [18], for reviews on the CCC). The study in the inhomogeneous dust collapse with a positive Λ, from the viewpoint of CCC, was examined in [6,19,20,21]. Deshingkar et al [19] showed that the presence of a Λ can cover a part of the singularity spectrum which is visible in the corresponding dust collapse models for the same initial data.…”

Section: Introductionmentioning

confidence: 99%

Higher dimensional dust collapse with a cosmological constant

Ghosh

Deshkar

2007

Astrophys Space Sci

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The general solution of the Einstein equation for higher dimensional (HD) spherically symmetric collapse of inhomogeneous dust in presence of a cosmological term, i.e., exact interior solutions of the Einstein field equations is presented for the HD Tolman-Bondi metrics imbedded in a de Sitter background. The solution is then matched to exterior HD Scwarschild-de Sitter. A brief discussion on the causal structure singularities and horizons is provided. It turns out that the collapse proceed in the same way as in the Minkowski background, i.e., the strong curvature naked singularities form and that the higher dimensions seem to favor black holes rather than naked singularities.

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Section: Introductionmentioning

confidence: 99%

Higher dimensional dust collapse with a cosmological constant

Ghosh

Deshkar

2007

Astrophys Space Sci

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“…It has recently been shown that a central, locally naked, Tipler strong singularity develops in the gravitational collapse of an inhomogeneous spherical dust with a positive cosmological constant [1,2]. Those results are a generalization to asymptotically de Sitter spacetimes of the well known asymptotically flat spherical dust (Lemaître-Tolman-Bondi (LTB)) collapse models.…”

Section: Introductionmentioning

confidence: 92%

“…The Szekeres metrics (with or without a cosmological constant) can be divided into two classes, depending on whether (Re ν ) vanishes or not [18,26]. The class defined by (Re ν ) = 0 contains shell-crossing singularities [28,29], which are physically 'mild'-they are gravitationally weak [30] and geodesically complete [31]-and hence will not be considered here. We shall focus on the class for which (Re ν ) = 0, which admits shellfocusing curvature singularities, but no shell-crossings.…”

Section: Szekeres Spacetimes With a Cosmological Constantmentioning

confidence: 99%

Strong curvature singularities in quasi-spherical asymptotically de Sitter dust collapse

Gonçalves¹

2001

Class. Quantum Grav.

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We study the occurrence, visibility, and curvature strength of singularities in dust-containing Szekeres spacetimes (which possess no Killing vectors) with a positive cosmological constant. We find that such singularities can be locally naked, Tipler strong and develop from a non-zero-measure set of regular initial data. When examined along timelike geodesics, the singularity's curvature strength is found to be independent of the initial data.

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“…In LTB collapse, shell crossing occurs for spatially inhomogeneous density distributions, whenever the proper time for collapse of a given shell is a monotonically decreasing function of the comoving radius. For the charged dust case, shell crossing has been shown to be inevitable, both for asymptotically flat [22], and asymptotically de Sitter [23] spacetimes. Physically, shell crossings signal the intersection of matter flow lines at a given spacelike surface, to the future of which the model therefore breaks down.…”

Section: Shell Crossingmentioning

confidence: 99%

Relativistic shells: Dynamics, horizons, and shell crossing

Gonçalves

2002

Phys. Rev. D

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We consider the dynamics of timelike spherical thin matter shells in vacuum. A general formalism for thin shells matching two arbitrary spherical spacetimes is derived, and subsequently specialized to the vacuum case. We first examine the relative motion of two dust shells by focusing on the dynamics of the exterior shell, whereby the problem is reduced to that of a single shell with different active Schwarzschild masses on each side. We then examine the dynamics of shells with non-vanishing tangential pressure p, and show that there are no stable-stationary, or otherwisesolutions for configurations with a strictly linear barotropic equation of state, p = ασ, where σ is the proper surface energy density and α ∈ (−1, 1). For arbitrary equations of state, we show that, provided the weak energy condition holds, the strong energy condition is necessary and sufficient for stability. We examine in detail the formation of trapped surfaces, and show explicitly that a thin boundary layer causes the apparent horizon to evolve discontinuously. Finally, we derive an analytical (necessary and sufficient) condition for neighboring shells to cross, and compare the discrete shell model with the well-known continuous Lemaître-Tolman-Bondi dust case.

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Shell crossing in generalized Tolman-Bondi spacetimes

Cited by 23 publications

References 18 publications

Higher dimensional dust collapse with a cosmological constant

Higher dimensional dust collapse with a cosmological constant

Strong curvature singularities in quasi-spherical asymptotically de Sitter dust collapse

Relativistic shells: Dynamics, horizons, and shell crossing

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