Dynamical extensions for shell-crossing singularities

Nolan, Brien C.

doi:10.1088/0264-9381/20/4/302

Cited by 24 publications

(32 citation statements)

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“…[51]. Moreover, solutions are extendable through shell-crossing singularities in a distributional sense [52,53]. In addition to this, energy density as well as the Ricci scalar can diverge when R = 0, giving rise to a shell-focusing or central singularity which is the main interest here.…”

Section: Classical Ltb Spacetimesmentioning

confidence: 99%

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Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity

2008

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Lemaitre-Tolman-Bondi models as specific spherically symmetric solutions of general relativity simplify in their reduced form some of the mathematical ingredients of black hole or cosmological applications. The conditions imposed in addition to spherical symmetry turn out to take a simple form at the kinematical level of loop quantum gravity, which allows a discussion of their implications at the quantum level. Moreover, the spherically symmetric setting of inhomogeneity illustrates several nontrivial properties of lattice refinements of discrete quantum gravity. Nevertheless, the situation at the dynamical level is quite non-trivial and thus provides insights to the anomaly problem. At an effective level, consistent versions of the dynamics are presented which implement the conditions together with the dynamical constraints of gravity in an anomaly-free manner. These are then used for analytical as well as numerical investigations of the fate of classical singularities, including non-spacelike ones, as they generically develop in these models. None of the corrections used here resolve those singularities by regular effective geometries. However, there are numerical indications that the collapse ends in a tamer shell-crossing singularity prior to the formation of central singularities for mass functions giving a regular conserved mass density. Moreover, we find quantum gravitational obstructions to the existence of exactly homogeneous solutions within this class of models. This indicates that homogeneous models must be seen in a wider context of inhomogeneous solutions and their reduction in order to provide reliable dynamical conclusions.

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Section: Classical Ltb Spacetimesmentioning

confidence: 99%

“…Shell-crossing singularities can be naked but gravitationally weak [100,101]. This singularity is so weak in curvature strength that it is generally believed to be extendible in a distributional sense [52,53]. Fig.…”

Section: Inverse Triad Corrections: First Versionmentioning

confidence: 99%

Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity

2008

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“…1 shows r 1 (t) > r 2 (t) at later times, i.e., the inner surface expands faster than the outer surface. This is the well-known "shell crossing" and leads to a spacetime singularity 21,22 , an obvious breakdown of the thin shell model. Now we argue that shell crossing is inevitable for dust thin shells.…”

Section: Validity Of Dust Thin Shell Models In Gravitational Collapsesmentioning

confidence: 99%

Validity of Thin Shell Models

Gao

2012

Int. J. Mod. Phys. Conf. Ser.

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The purpose of this paper is to test the validity of the thin shell formalism. Firstly, we construct a dust thick shell collapsing to a Schwarzschild black hole. From this exact solution, we show that the two sides of the shell satisfy different equations of motion. Moreover, we show that the inner side and the outer side always cross each other right after the formation of the thin shell, causing a breakdown of the model. Secondly, we establish a class of wormholes with non-zero thickness and extremal Reissner-Nordström exterior. In the thin shell limit, we find that the surface stress-energy tensor contains the contribution of electromagnetic field, which contradicts the assumption in previous literature.

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“…If two of these shells collide then the intermediate shells are trapped between them, so that the matter density is forced to blow up. For more information about shell-crossing singularities see for instance [7] and references therein. For general plane symmetric solutions of the Einstein-dust system it must be expected that shell-crossing singularities develop, even from smooth initial data.…”

Section: Introductionmentioning

confidence: 99%