Strong Cosmic Censorship in orthogonal Bianchi class B perfect fluids and vacuum models

Radermacher, Katharina Maria

doi:10.48550/arxiv.1612.06278

Cited by 3 publications

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“…409] (since we appeal to the results of [RinAtt] quite frequently in the present paper). In the case of Bianchi class B, the division into types can be found in, e.g., [RadNon,Table 1,p. 16] (again, we appeal to the results of [RadNon] quite frequently in the present paper).…”

Section: Main Energy Estimatementioning

confidence: 99%

“…The reason for this is that if one considers (given a left invariant Riemannian initial metric) the momentum constraint as a linear equation for a left invariant second fundamental form, then this equation has a degeneracy which occurs exactly for Bianchi type VI −1/9 ; cf. [RadNon,Subsection 11.3,, in particular [RadNon,Lemma 11.13,p. 63], for more details.…”

Section: Main Energy Estimatementioning

confidence: 99%

“…In particular, if 1 ≤ γ ≤ 2, then Bianchi type IX developments have monotone volume singularities both to the future and to the past. [RadNon,Lemma 11.16,p. 71], it either has θ(t) > 0 for all t ∈ I, or it arises from initial data whose universal covering space is initial data for Minkowski space; Bianchi type I is included in the framework of [RadNon].…”

Section: Geometric Properties Of Bianchi Developmentsmentioning

confidence: 99%

“…The reader interested in a justification of these statements is referred to [RadNon,Subsection 11.5, (the τ appearing in [RadNon] can be assumed to coincide with the τ of the present paper; cf. the beginning of Subsection 17.2).…”

Section: Geometric Properties Of Bianchi Developmentsmentioning

confidence: 99%

“…Finally, note that a Bianchi class B development with ρ = 0 or with ρ > 0 and 0 < γ ≤ 2 is past causally geodesically incomplete and future causally geodesically incomplete; cf. [RadNon,Lemma 11.20,p. 74].…”

Section: Geometric Properties Of Bianchi Developmentsmentioning

confidence: 99%

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A Unified Approach to the Klein–Gordon Equation on Bianchi Backgrounds

Ringström

2019

Commun. Math. Phys.

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In this paper, we study solutions to the Klein-Gordon equation on Bianchi backgrounds. In particular, we are interested in the asymptotic behaviour of solutions in the direction of silent singularities. The main conclusion is that, for a given solution u to the Klein-Gordon equation, there are smooth functions u i , i = 0, 1, on the Lie group under consideration, such that uσ(·, σ) − u 1 and u(·, σ) − u 1 σ − u 0 asymptotically converge to zero in the direction of the singularity (where σ is a geometrically defined time coordinate such that the singularity corresponds to σ → −∞). Here u i , i = 0, 1, should be thought of as data on the singularity. Interestingly, it is possible to prove that the asymptotics are of this form for a large class of Bianchi spacetimes. Moreover, the conclusion applies for singularities that are matter dominated; singularities that are vacuum dominated; and even when the asymptotics of the underlying Bianchi spacetime are oscillatory. To summarise, there seems to be a universality as far as the asymptotics in the direction of silent singularities are concerned. In fact, it is tempting to conjecture that as long as the singularity of the underlying Bianchi spacetime is silent, then the asymptotics of solutions are as described above. In order to contrast the above asymptotics with the non-silent setting, we, by appealing to known results, provide a complete asymptotic characterisation of solutions to the Klein-Gordon equation on a flat Kasner background. In that setting, uσ does, generically, not converge.

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Section: Main Energy Estimatementioning

confidence: 99%

Section: Main Energy Estimatementioning

confidence: 99%

Section: Geometric Properties Of Bianchi Developmentsmentioning

confidence: 99%

Section: Geometric Properties Of Bianchi Developmentsmentioning

confidence: 99%

Section: Geometric Properties Of Bianchi Developmentsmentioning

confidence: 99%

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A Unified Approach to the Klein–Gordon Equation on Bianchi Backgrounds

Ringström

2019

Commun. Math. Phys.

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Chaotic Dynamics of Spatially Homogeneous Spacetimes

Béguin

Dutilleul

2022

Commun. Math. Phys.

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Orthogonal Bianchi B stiff fluids close to the initial singularity

Radermacher

2017

Preprint

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In our previous article [Rad16], we investigated the asymptotic behaviour of orthogonal Bianchi class B perfect fluids close to the initial singularity and proved the Strong Cosmic Censorship conjecture in this setting. In several of the statements, the case of a stiff fluid had to be excluded. The present paper fills this gap.We work in expansion-normalised variables introduced by Hewitt-Wainwright and find that solutions converge, but show a convergence behaviour very different from the non-stiff case: All solutions tend to limit points in the two-dimensional Jacobs set. A set of full measure, which is also a countable intersection of open and dense sets in the state space, yields convergence to a specific subset of the Jacobs set.

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Strong Cosmic Censorship in orthogonal Bianchi class B perfect fluids and vacuum models

Cited by 3 publications

References 0 publications

A Unified Approach to the Klein–Gordon Equation on Bianchi Backgrounds

A Unified Approach to the Klein–Gordon Equation on Bianchi Backgrounds

Chaotic Dynamics of Spatially Homogeneous Spacetimes

Orthogonal Bianchi B stiff fluids close to the initial singularity

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