On the dynamics of the general Bianchi IX spacetime near the singularity

Kiefer, Claus; Kwidzinski, Nick; Piechocki, Włodzimierz

doi:10.1140/epjc/s10052-018-6155-8

Cited by 23 publications

(38 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is generally believed that the approach to a spacelike singularity at the level of the full Einstein equations can be described by the Belinsky-Khalatnikov-Lifshits (BKL) scenario; see, for example, [26,37] and references therein. This corresponds to a decoupling of spatial points, in which every spatial point exhibits the dynamics of a separate Bianchi IX model.…”

Section: Discussionmentioning

confidence: 99%

Singularity avoidance in Bianchi I quantum cosmology

2019

Self Cite

View full text Add to dashboard Cite

We extend recent discussions of singularity avoidance in quantum gravity from isotropic to anisotropic cosmological models. The investigation is done in the framework of quantum geometrodynamics (Wheeler-DeWitt equation). We formulate criteria of singularity avoidance for general Bianchi class A models and give explicit and detailed results for Bianchi I models with and without matter. The singularities in these cases are big bang and big rip. We find that the classical singularities can generally be avoided in these models. I. INTRODUCTIONA major issue in any quantum theory of gravity is the fate of the classical singularities. So far, such a theory is not available in final form, although various approaches exist in which this question can be sensibly addressed [1,2]. It is clear that such an investigation cannot yet be done at the level of mathematical rigor comparable to the singularity theorems in the classical theory (see e.g. [3]). Nevertheless, focusing on concrete approaches and concrete models, one can state criteria of singularity avoidance and discuss their implementation. This is what we shall do here.We restrict our analysis of singularity avoidance to quantum geometrodynamics, with the Wheeler-DeWitt equation as its central equation [1]. Although this may not be the most fundamental level of quantum gravity, it is sufficient for addressing the issue of singularity avoidance. Quantum geometrodynamics follows directly from general relativity by rewriting the Einstein equations in Hamilton-Jacobi form and formulating quantum equations that yield the Hamilton-Jacobi equations in the semiclassical (WKB) limit. It thus makes as much sense to addressing singularity avoidance here than it does to addressing it in quantum mechanics at the level of the Schrödinger equation. Singularity avoidance has also been discussed in loop quantum gravity [2,4,5], with various results, but we will not consider this here.Singularity avoidance was already addressed by DeWitt in his pioneering paper on canonical quantum gravity [6]. He suggested to impose the condition Ψ → 0 for the quantum-gravitational wave functional Ψ when approaching the region of a classical singularity. The wave functional is effectively defined on the configuration space of all threedimensional geometries, also called superspace [1,7]. The "DeWitt criterion" of vanishing wave function then means that Ψ must approach zero when approaching a singular three-geometry (which itself is not part of superspace, but can be envisaged as its boundary). It is important to emphasize that this criterion is a sufficient but not a necessary one: singularities can be avoided for non-vanishing or even diverging Ψ (recall the ground state solution of the Dirac equation for the hydrogen atom, which diverges).DeWitt had in mind cosmological singularities such as big bang or big crunch. The DeWitt criterion applies, of course, also to the singularities that classically arise from gravitational collapse. In simple models of quantum geometrodynamics, their avoidance can be...

show abstract

Section: Discussionmentioning

confidence: 99%

Singularity avoidance in Bianchi I quantum cosmology

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…The expansion scalar is given by FIG . 1: Plot (a) shows the result of the application of the shooting method described in [1] "close" to the recollapse (which is roughly at t ≈ −1000). The plot (b) was obtained from a numerical calculation based on the result of section III.…”

Section: Calculation Of the Kretschmann Scalarmentioning

confidence: 99%

“…Moreover, the Hamiltonian formulation can be employed to obtain a qualitative picture of the dynamics (see e.g. [1,[14][15][16]19]).…”

Section: Hamiltonian Formulation Of the Dust Filled Bianchi IX Modelmentioning

confidence: 99%

“…This case might be considered as the most generic one in the context of the model under consideration. For convenience, we restrict ourselves in this work to the numerical solution which was already considered in [1]. The part of the solution plotted in Fig.…”

Section: Hamiltonian Formulation Of the Dust Filled Bianchi IX Modelmentioning

confidence: 99%

“…For our variables this means that the dust velocities v i assume constant values. The main purpose of the article [1] was to provide a numerical verification for the two assumptions. According to the phrase "matter does not matter" we expect the matter terms in the Kretschmann scalar to be negligible in the asymptotic regime, that is, the Weyl part should dominate over the Ricci part.…”

Section: The Asymptotic Regime Close To the Singularitymentioning

confidence: 99%

See 2 more Smart Citations

Curvature invariants for the Bianchi IX spacetime filled with tilted dust

Kwidzinski

Piechocki

2019

Eur. Phys. J. C

Self Cite

View full text Add to dashboard Cite

show abstract

Bianchi IX geometry and the Einstein–Maxwell theory

Ghezelbash

2022

Class. Quantum Grav.

View full text Add to dashboard Cite

We construct numerical solutions to the higher-dimensional Einstein-Maxwell theory. The solutions are based on embedding the four dimensional Bianchi type IX space in the theory. We ﬁnd the solutions as superposition of two functions, which one of them can be found numerically. We show that the solutions in any dimensions, are almost regular everywhere, except a singular point. We ﬁnd that the solutions interpolate between the two exact analytical solutions to the higher dimensional Einstein-Maxwell theory, which are based on Eguchi-Hanson type I and II geometries. Moreover, we construct the exact cosmological solutions to the theory, and study the properties of the solutions.

show abstract

On the dynamics of the general Bianchi IX spacetime near the singularity

Cited by 23 publications

References 38 publications

Singularity avoidance in Bianchi I quantum cosmology

Singularity avoidance in Bianchi I quantum cosmology

Curvature invariants for the Bianchi IX spacetime filled with tilted dust

Bianchi IX geometry and the Einstein–Maxwell theory

Contact Info

Product

Resources

About