Rotating dust solutions of Einstein’s equations with three-dimensional symmetry groups. III. All Killing fields linearly independent of uα and wα

Krasiński, Andrzej

doi:10.1063/1.532302

Cited by 19 publications

(19 citation statements)

References 109 publications

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“…As seen from (6.1), the symmetry group becomes Bianchi type I in the limit ω 0 → 0 after the reparametrization (6.4) (the Killing field k (3) has to be replaced by l (3) = ω 0 k (3) in order that the limit is nonsingular).…”

Section: Cases 12 and 2 Of Refmentioning

confidence: 99%

“…(3.7) -(3.11) in Ref. 3. It is of Bianchi type VIII or VI 0 (when g = 0 or g = 0, respectively), so only the k = 0 Friedmann limit may exist here.…”

Section: Cases 12 and 2 Of Refmentioning

confidence: 99%

“…4: In the cases considered in Ref. 3, each of the 3 Killing vectors is linearly independent of the velocity and rotation. However, the 5 vectors existing in each 4-dimensional tangent space to the manifold cannot form a linearly independent set.…”

Section: Cases 12 and 2 Of Refmentioning

confidence: 99%

“…Before the limit D → 0 can be taken, k (3) needs to be redefined by k ′ (3) = (1/D)k (3) . The basis in the limit becomes:…”

Section: Cases 12 and 2 Of Refmentioning

confidence: 99%

“…When all 3 Killing fields are of the general type, all the Bianchi types appear, some of them hidden as limits of more general types (Ref. 3). …”

mentioning

confidence: 99%

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Friedmann limits of rotating hypersurface–homogeneous dust models

Krasiński

2001

Journal of Mathematical Physics

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The existence of Friedmann limits is systematically investigated for all the hypersurface-homogeneous rotating dust models, presented in previous papers by this author. Limiting transitions that involve a change of the Bianchi type are included. Except for stationary models that obviously do not allow it, the Friedmann limit expected for a given Bianchi type exists in all cases. Each of the 3 Friedmann models has parents in the rotating class; the k = +1 model has just one parent class, the other two each have several parent classes. The type IX class is the one investigated in 1951 by Gödel. For each model, the consecutive limits of zero rotation, zero tilt, zero shear and spatial isotropy are explicitly calculated.I. Motivation and summary of the method.In previous papers 1−3 a complete set of all metric forms was derived that can represent hypersurface-homogeneous rotating dust models. For each case, the generators of the symmetry algebra were found, the Bianchi type determined, and the metric form resulting from the Killing equations was explicitly presented. That classification was more detailed than the Bianchi classification because all possible orientations of the symmetry orbits in the spacetime were allowed, i.e. the orbits could be spacelike, timelike or null.In a later paper 4 , one of the Bianchi type V models was investigated. Among the problems considered there was the question whether the model can reproduce the k = −1 Friedmann model in the limit of zero rotation, ω → 0. Since the coordinates that are well-suited to the classification are not suitable at all for considering the limit ω → 0, this limit could be taken only after a coordinate change and reparametrization of the metric.In the present paper, the existence of the Friedmann limits is systematically investigated for all the other cases found in the classification in Refs. 1-3. The Bianchi type is allowed to change in the limiting transition. In all Bianchi type I cases the velocity field is tangent to the symmetry orbits, i.e. those models have matter density constant along the flow, and *

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Section: Cases 12 and 2 Of Refmentioning

confidence: 99%

“…(3.7) -(3.11) in Ref. 3. It is of Bianchi type VIII or VI 0 (when g = 0 or g = 0, respectively), so only the k = 0 Friedmann limit may exist here.…”

Section: Cases 12 and 2 Of Refmentioning

confidence: 99%

Section: Cases 12 and 2 Of Refmentioning

confidence: 99%

“…Before the limit D → 0 can be taken, k (3) needs to be redefined by k ′ (3) = (1/D)k (3) . The basis in the limit becomes:…”

Section: Cases 12 and 2 Of Refmentioning

confidence: 99%

“…When all 3 Killing fields are of the general type, all the Bianchi types appear, some of them hidden as limits of more general types (Ref. 3). …”

mentioning

confidence: 99%

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Friedmann limits of rotating hypersurface–homogeneous dust models

Krasiński

2001

Journal of Mathematical Physics

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Closed timelike loops in homogeneous rotating $$\varLambda $$ Λ -dust cosmologies

Lindsay

2015

Gen Relativ Gravit

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Gödel-type universes and chronology protection in Hořava–Lifshitz gravity

2013

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In the attempts toward a quantum gravity theory, general relativity faces a serious difficulty since it is non-renormalizable theory. Hořava-Lifshitz gravity offers a framework to circumvent this difficulty, by sacrificing the local Lorentz invariance at ultra-high energy scales in exchange of power-counting renormalizability. The Lorentz symmetry is expected to be recovered at low and medium energy scales. If gravitation is to be described by a Hořava-Lifshitz gravity theory there are a number of issues that ought to be reexamined in its context, including the question as to whether this gravity incorporates a chronology protection, or particularly if it allows Gödel-type solutions with violation of causality. We show that Hořava-Lifshitz gravity only allows hyperbolic Gödeltype space-times whose essential parameters m and ω are in the chronology respecting intervals, excluding therefore any noncausal Gödel-type space-times in the hyperbolic class. There emerges from our results that the famous noncausal Gödel model is not allowed in Hořava-Lifshitz gravity. The question as to whether this quantum gravity theory permits hyperbolic Gödel-type solutions in the chronology preserving interval of the essential parameters is also examined. We show that Hořava-Lifshitz gravity not only excludes the noncausal Gödel universe, but also rules out any hyperbolic Gödel-type solutions for physically well-motivated perfect-fluid matter content.PACS numbers: 95.30. Sf, 98.80.Jk, 04.50.Kd, 95.36.+x

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Rotating dust solutions of Einstein’s equations with three-dimensional symmetry groups. III. All Killing fields linearly independent of uα and wα

Cited by 19 publications

References 109 publications

Friedmann limits of rotating hypersurface–homogeneous dust models

Friedmann limits of rotating hypersurface–homogeneous dust models

Closed timelike loops in homogeneous rotating $$\varLambda $$ Λ -dust cosmologies

Gödel-type universes and chronology protection in Hořava–Lifshitz gravity

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