Gravitational collapse with non-vanishing tangential stresses: a generalization of the Tolman - Bondi model

Magli, Giulio

doi:10.1088/0264-9381/14/7/026

Cited by 90 publications

(110 citation statements)

References 25 publications

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“…We have introduced a function h = h(r, R) ≥ 0 as 8) where the comma denotes the partial derivative. We should note that the definition of h is slightly different from Magli (1997Magli ( , 1998)'s notation. The dust limit is given by h = h(r).…”

Section: )mentioning

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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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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Section: )mentioning

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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“…In this context, Magli [9] examined this model again. He discussed a general class of spherically symmetric solutions to Einstein's equations with vanishing radial pressure.…”

Section: Introductionmentioning

confidence: 99%

Spherical universes with anisotropic pressure

Gair

2001

Class. Quantum Grav.

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Abstract. Einstein's equations are solved for spherically symmetric universes composed of dust with tangential pressure provided by angular momentum, L(R), which differs from shell to shell. The metric is given in terms of the shell label, R, and the proper time, τ , experienced by the dust particles. The general solution contains four arbitrary functions of R -M (R), L(R), E(R) and τ 0 (R). The solution is described by quadratures, which are in general elliptic integrals. It provides a generalization of the Lemaître-Tolman-Bondi solution. We present a discussion of the types of solution, and some examples. The relationship to Einstein clusters and the significance for gravitational collapse is also discussed.

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“…In this section we review briefly the main properties of spherically symmetric gravitating systems with vanishing radial stresses (for details, see [6,7]). …”

Section: Spherical Collapse With Tangential Stressesmentioning

confidence: 99%

“…A model in which analytical treatment appears feasible is that of vanishing radial stresses, since in this case the general exact solution is known in closed form [6,7] (the opposite case, in which only a radial stress is present, has also been recently considered [8]). The formation and nature of singularities in gravitational collapse with tangential stresses has recently been studied quite extensively [9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

Spectrum of end states of gravitational collapse with tangential stresses

2002

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The final state-black hole or naked singularity-of the gravitational collapse of a marginally bound matter configuration in the presence of tangential stresses is classified, in full generality, in terms of the initial data and equation of state. If the tangential pressure is sufficiently strong, configurations that would otherwise evolve to a spacelike singularity, result in a locally naked singularity, both in the homogeneous and in the general, inhomogeneous density case.

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Gravitational collapse with non-vanishing tangential stresses: a generalization of the Tolman - Bondi model

Cited by 90 publications

References 25 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

Spherical universes with anisotropic pressure

Spectrum of end states of gravitational collapse with tangential stresses

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