Qualitative Cosmology

Collins, C. B.; Stewart, J. M.

doi:10.1093/mnras/153.4.419

Cited by 112 publications

(102 citation statements)

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“…III. Finally the following three distinct PMpf solutions are particular cases of the general LRS cases above: the p = 1 5 µ Collins-Stewart space-time [33] and Lozanovski-Aarons metric [29], both LRS class III, and the LRS class I rigidly rotating axistationary model with circular motion of [34]. The last example was found within a study (regardless of the Petrov type) of axistationary perfect fluids, which concentrated mostly on the PMpf subclass.…”

Section: Introductionmentioning

confidence: 83%

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Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Wylleman

Bergh

2006

Phys. Rev. D

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Recently the class of purely magnetic non-rotating dust spacetimes has been shown to be empty (Wylleman, Class. Quant. Grav. 23, 2727). It turns out that purely magnetic rotating dust models are subject to severe integrability conditions as well. One of the consequences of the present paper is that also rotating dust cannot be purely magnetic when it is of Petrov type D or when it has a vanishing spatial gradient of the energy density. For purely magnetic and non-rotating perfect fluids on the other hand, which have been fully classified earlier for Petrov type D (Lozanovski, Class. Quant. Grav. 19, 6377), the fluid is shown to be non-accelerating if and only if the spatial density gradient vanishes. Under these conditions, a new and algebraically general solution is found, which is unique up to a constant rescaling, which is spatially homogeneous of Bianchi type V I0, has degenerate shear and is of Petrov type I(M ∞ ) in the extended Arianrhod-McIntosh classification.The metric and the equation of state are explicitly constructed and properties of the model are briefly discussed. We finally situate it within the class of normal geodesic flows with degenerate shear tensor.

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Section: Introductionmentioning

confidence: 83%

“…Taking an orthonormal eigenframe B of H ab , we may assume that H 22 = H 33 . In this case the (22), (33) and (23) components of (25), (26) immediately give q 1 = −r 1 , σ 23 = 0, n 33 = n 22 and h 1 = 0 (such that h 3 = −h 2 ), while the (12), and (13) components of (25), (26) together with the (2,3) components of (24) lead to…”

Section: Proofmentioning

confidence: 99%

Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Wylleman

Bergh

2006

Phys. Rev. D

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“…Another special solution which will play an important role is the Collins-Stewart solution ( [6], p. 430) with dust (γ = 1) which has Bianchi II symmetry:…”

Section: The Collins-stewart Solutionmentioning

confidence: 99%

Future Non-Linear Stability for Reflection Symmetric Solutions of the Einstein–Vlasov System of Bianchi Types II and VI0

Nungesser

2012

Ann. Henri Poincaré

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Using the methods developed for the Bianchi I case we have shown that a boostrap argument is also suitable to treat the future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0. These solutions are asymptotic to the Collins-Stewart solution with dust and the Ellis-MacCallum solution respectively. We have thus generalized the results obtained by Rendall and Uggla in the case of locally rotationally symmetric Bianchi II spacetimes to the reflection symmetric case. However we needed to assume small data. For Bianchi VI0 there is no analogous previous result.

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“…The evolution equations for the dimensionless gravitational field variables follow from equations (1.90)-(1.98) in WE, using (5)- (8).…”

Section: Extended Orthonormal Frame Approachmentioning

confidence: 99%

“…There are also two variables with dimension, namely the Hubble scalar H and the particle energy E. These scalars satisfy the decoupled equations (8) and (14). They are thus determined by quadrature once a solution of the extended system of equations has been found.…”

Section: Structure Of the Extended System Of Equationsmentioning

confidence: 99%

A Dynamical Systems Approach to Geodesics in Bianchi Cosmologies

Nilsson

Uggla

Wainwright

2000

General Relativity and Gravitation

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To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the orthonormal frame approach, has proved to be an invaluable tool for analyzing spatially homogeneous cosmologies. It is thus natural to use such techniques to study the geodesics of these models. We therefore augment the Einstein field equations with the geodesic equations, all written in dimensionless form, obtaining an extended system of first-order ordinary differential equations that simultaneously describes the evolution of the gravitational field and the behavior of the associated geodesics. It is shown that the extended system is a powerful tool for investigating the effect of spacetime anisotropies on the temperature of the cosmic microwave background radiation, and that it can also be used for studying geodesic chaos.

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Qualitative Cosmology

Cited by 112 publications

References 0 publications

Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Future Non-Linear Stability for Reflection Symmetric Solutions of the Einstein–Vlasov System of Bianchi Types II and VI0

A Dynamical Systems Approach to Geodesics in Bianchi Cosmologies

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