Shell crossing in generalized Tolman-Bondi spacetimes

Sergio M. C. V. Goncalves (Caltech)

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Shell crossing in generalized Tolman-Bondi spacetimes

General Relativity and Quantum Cosmology · Submitted 26 Jul 2001

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Physically reasonable initial data inevitably leads to shell crossing (near the center) before the minimum bounce radius is reached.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.07 · mentions code or data availability 0.01.

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We study the occurrence of shell crossing in spherical weakly charged dust collapse in the presence of a non-vanishing cosmological constant. We find that shell crossing always occurs from generic time-symmetric regular initial data, near the center of the matter configuration. For non-time-symmetric initial data, the occurrence---or lack thereof---of shell crossing is determined by the initial velocity profile, for a given mass and charge distribution. Physically reasonable initial data inevitably leads to shell crossing (near the center) before the minimum bounce radius is reached.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the occurrence of shell crossing in spherical weakly charged dust collapse in the presence of a non-vanishing cosmological constant.	contribution 0.98	0.86	0.06	unclear 0.62
s1	We find that shell crossing always occurs from generic time-symmetric regular initial data, near the center of the matter configuration.	result 1.00	0.96	0.48	asserted 1.00
s2	For non-time-symmetric initial data, the occurrence---or lack thereof---of shell crossing is determined by the initial velocity profile, for a given mass and charge distribution.	result 1.00	0.86	0.17	asserted 1.00
s3	Physically reasonable initial data inevitably leads to shell crossing (near the center) before the minimum bounce radius is reached.	result 0.83	0.85	0.51	asserted 1.00

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Original abstract

We study the occurrence of shell crossing in spherical weakly charged dust collapse in the presence of a non-vanishing cosmological constant. We find that shell crossing always occurs from generic time-symmetric regular initial data, near the center of the matter configuration. For non-time-symmetric initial data, the occurrence---or lack thereof---of shell crossing is determined by the initial velocity profile, for a given mass and charge distribution. Physically reasonable initial data inevitably leads to shell crossing (near the center) before the minimum bounce radius is reached.

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6 arXiv papers cite this in 10 sentences

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Uses its method or tool 1 paper

Consider the Lemaitre-Tolman-Bondi (LTB) formalism [ref] , starting from metric: [equation] which only assumes spherical symmetry.

Dark matter and space-time symmetry restoration · “Painted on” dark matter and testability · 0.81

Cites it as background 3 papers

This then raised the question of the continuity of the metric across these singularities and, very interestingly, solutions of dynamical extension through shell crossing singularities of LTB have been proved to exist, by Nolan [ref] , while the case including a cosmological constant and electric charges has been discussed by Gon�alves [ref] .

The role of shell crossing on the existence and stability of trapped matter shells in spherical inhomogeneous \Lambda-CDM models · Introduction · 0.81
The Lemaitre metric, as presented in [ref] , takes the form: [equation] where $A$ is the areal radius and prime denotes the derivative with respect to the coordinate $r$.

Violations of energy conservation in Horava-Lifshitz gravity: a new ingredient in the dark matter puzzle · A test tube: the Schwarzschild solution in Lemaitre coordinates · 0.80
Solutions of dynamical extension through shell crossing singularities of simple dust have been found by Nolan [ref] , while the case including also a cosmological constant and electric charges have been discussed by Goncalves [ref] .

Local conditions separating expansion from collapse in spherically symmetric models with anisotropic pressures · Introduction · 0.82

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