Within the scope of anisotropic non-diagonal Bianchi type-II, VIII and IX spacetime it is shown that the off-diagonal components of the corresponding metric impose severe restrictions on the components of the energy momentum tensor in general. If the energy momentum tensor is considered to be diagonal one, the spacetime, expect a partial case of BII, becomes locally rotationally symmetric.
Bianchi models are posited by the BKL picture to be essential building blocks towards an understanding of generic cosmological singularities. We study the behaviour of spatially homogeneous anisotropic vacuum spacetimes of Bianchi type VIII and IX, as they approach the big bang singularity. It is known since 2001 that generic Bianchi IX spacetimes converge towards the so-called Mixmaster attractor as time goes towards the singularity. We extend this result to the case of Bianchi VIII vacuum. The BKL picture suggests that particle horizons should form, i.e. spatially separate regions should cau…
In this paper we present the quantum LRS Bianchi IX models or, as they may be better known, the Taub-NUT models in addition to the quantum LRS Bianchi VIII models, both coupled to a stiff matter source. We solve their Wheeler DeWitt equations for an arbitrary Hartle-Hawking ordering parameter using separation of variables. Afterwards we construct a superposition of their respective wave functions and discuss some of the interesting qualitative properties they possess.
We consider the most general form of Bianchi types VIII and IX space-times for studying proper affine symmetry by using holonomy and decomposability, the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper affine symmetry in the above space-times it is shown that there exists only one possibilty when the above space-times admit proper affine vector field.
In this paper we study the exact solutions for a viscous fluid distribution in Bianchi II, VIII, and IX models. The metric is simplified by assuming a relationship between the coefficients and the metric tensor. Solutions are obtained in two special cases: in one, an additional assumption is made where the matter density and the expansion scalar have a definite relation and in the other a barotropic equation of state between the matter density and the thermodynamic pressure is assumed. While the Bianchi II solutions are already found in the literature the other two classes of solutions are app…
In the present work we revisit the axisymmetric Bianchi VIII and IX models. At the classical level we reproduce the known analytic solution, in a novel way making use of two quadratic integrals of motion, the constraint equation, as well as a linear non-local integral of motion. These quantities correspond to two second rank Killing tensors and a homothetic vector field existing on the relevant configuration space. On the corresponding phase space the two quadratic charges commute with the Hamiltonian constraint but not among themselves. Thus, after turning these charges into operators we obta…
New non trivial solutions to the Lorentzian-signature symmetry reduced Bianchi VIII Wheeler DeWitt equation for Hartle Hawking ordering parameters $ \pm 2\sqrt{33} $ are obtained using an Euclidean-signature semi classical method. Using the aforementioned method we define 'excited' states for the Bianchi VIII wave function and construct leading order 'excited' states which appear to be a hybrid of scattering and bound states. Also six new solutions for the $Λ\ne 0$ Bianchi VIII Euclidean-signature Hamilton Jacobi equation are presented which can be used to construct semi-classical states corre…
Global existence to the coupled Einstein-Maxwell system which rules the dynamics of a kind of charged matter with a pseudo-tensor of pressure is proved, in Bianchi I-VIII spacetimes. We study the geodesics completeness, the asymptotic behavior, the positivity conditions, and we prove that the problem is well-posed in the sense of Hadamard.
We investigate the quantum cosmologies of the Bianchi IX and VIII models when a cosmological constant, aligned electromagnetic field and free scalar field are present. The conserved quantity $p_ϕ$ associated with our free scalar field results in $ϕ$ classically being a quantity which monotonically increases with respect to time, thus allowing it to fulfill the role of an 'emergent' internal clock for our constrained quantum systems. We embark on this investigation to better understand how matter sources can affect general anisotropic quantum cosmologies. To aid us we use the Euclidean-signatur…
Scalar fields on SL(2,R) and H^2 x R geometric spacetimes and linear perturbations
利用适当的调和函数，研究了一类宇宙真空时空中无质量标量场的未来渐近行为。假设空间流形是高亏格曲面上具有局部齐次度量的圆丛。这样的流形对应于SL（2，R）-几何（Bianchi VIII型）或H^2 x R-几何（Bianchi III型）。经过技术准备，包括引入合适的谐波圆纤维比安奇八分离变量，我们推导出系统的常微分方程的标量场。我们提出了未来的渐近解这些方程在一个特殊的情况下，并发现有一个密切的相似之处，圆纤维比安奇III时空。我们讨论这种相似性的影响，特别是（引力）线性扰动。我们还指出，这种相似性可以解释为“纤维项主导的行为”的两个模型。
Solutions have been found for gravity coupled to electromagnetic field and a set of charged and uncharged perfect fluids for Bianchi Types VI_{(-1)}, VIII, IX, under the primary assumption of the existence of a conformal Killing vector field. The electromagnetic field ``absorbs'' the ``frozen'' anisotropy and the remaining equations are dynamically equivalent with the equations of ΛCDM. There are solutions with flat, negative and positive effective spatial curvature corresponding to the three FLRW classes. Three equations of state for the charged perfect fluid where studied: non-relativistic w…
Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in the basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking non-diagonal Einstein metrics, and we find solutions which in some cases exhaust the possibilities. In particular we construct new examples of neutral signature non--diagonal Bianchi type VIII Einstein metrics with self--dual Weyl tensor.
We explore the entire form of S-Matrix elements of a potential $C_{n-1}$ Ramond-Ramond (RR) form field, a tachyon and two transverse scalar fields on both world volume and transverse directions of type IIB and IIA superstring theories. Apart from $<V_{C^{-2}}V_{ϕ^{0}}V_{ϕ^{0}}V_{T ^{0}}>$ the other scattering amplitude, namely $<V_{C^{-1}}V_{ϕ^{-1}}V_{ϕ^{0}}V_{T ^{0}}>$ is also revealed. We then start to compare all singularity structures of symmetric and asymmetric analysis, generating all infinite singularity structures as well as all order $α'$ contact interactions on the whole directions. …
