Kantowski-Sachs Spacetimes Research Articles

Quantum field theory of the Universe in the Kantowski-Sachs space-time

In this paper, the quantum field theory of the Universe in the Kantowski-Sachs space-time is studied. We apply an analogue of proceeding in quantum field theory in curved space-time to the Kantowski-Sachs space-time, and obtain the wave function of the Universe satisfied the Wheeler-De Witt equation. Regarding the wave function as a universe field in the minisuperspace, we can not only overcome the difficulty of the probabilistic interpretation in quantum cosmology, but also come to the conclusion that there is multiple production of universes. The average number of the produced universes from «nothing» is calculated. The distribution of created universes is given. We find that it is the Planckian distribution.

Wormholes as a basis for the Hilbert space in Lorentzian gravity

We carry out to completion the quantization of a Friedmann-Robertson-Walker model provided with a conformal scalar field, and of a Kantowski-Sachs spacetime minimally coupled to a massless scalar field. We prove that the Hilbert space determined by the reality conditions that correspond to Lorentzian gravity admits a basis of wormhole wave functions. This result implies that the vector space spanned by the quantum wormholes can be equipped with an unique inner product by demanding an adequate set of Lorentzian reality conditions, and that the Hilbert space of wormholes obtained in this way can be identified with the whole Hilbert space of physical states for Lorentzian gravity. In particular, all the normalizable quantum states can then be interpreted as superpositions of wormholes. For each of the models considered here, we finally show that the physical Hilbert space is separable by constructing a discrete orthonormal basis of wormhole solutions.

WORMHOLE SOLUTIONS IN THE KANTOWSKI-SACHS SPACE-TIME

I present quantum wormhole solutions in the Kantowski-Sachs space-time generated from coupling the gravitational field to the axion and EM fields. These solutions correspond to the classical ones found by Keay and Laflamme and by Cavaglià et al.

Quantum cosmology of openR x S2 x S1.

We examine the classical and quantum cosmology of a Kantowski-Sachs spacetime manifold with a topology openR\ifmmode\times\else\texttimes\fi{}${\mathit{S}}^{2}$\ifmmode\times\else\texttimes\fi{}${\mathit{S}}^{1}$ and a nonzero cosmological constant, within the framework of canonical quantum gravity. The classical trajectories are analyzed, and it is shown that the classical problem can be reduced to that of free particles. Both the Hartle-Hawking ``no-boundary'' proposal and the Vilenkin ``outgoing flux'' proposal are examined. First, the Hartle-Hawking proposal is generalized to canonical quantum gravity by imposing generic initial conditions on the solutions to the Wheeler-DeWitt equation at small scale factors. The resulting wave function has essentially the same leading exponential behavior as the semiclassical approximation to the ``no-boundary'' Euclidean functional integral in the nonoscillatory region. It is further shown, by calculating overlap integrals with semiclassical wave functions, that the wave function diverges too quickly in this region to be interpreted probabilistically. An analogue of the Baum-Hawking factor appears, and is interpreted as indicating that, given a small \ensuremath{\Lambda}, the wave function is highly peaked around a class of configurations in which the ${\mathit{S}}^{2}$ radius is R=[1/(2G${\mathrm{\ensuremath{\Lambda}}}^{1/2}$)]. These configurations are classically unstable. Second, given a complete set of solutions to the Wheeler-DeWitt equation, the outgoing flux proposal is found to be insufficient to select a unique wave function. A source is found for the Wheeler-DeWitt current of the above solutions. No analogue of the Baum-Hawking factor appears in the outgoing flux model.

Bianchi type III and Kantowski-Sachs cosmological models in Lyra geometry

Cosmological models for Bianchi type III and Kantowski-Sachs space-times within the framework of Lyra geometry are obtained. The physical behavior of the models is also discussed.

Incompleteness theorems for the spherically symmetric spacetimes.

The closed-universe recollapse conjecture is studied for the spherically symmetric spacetimes. It is proven that there exists an upper bound to the lengths of timelike curves in any spherically symmetric spacetime that possesses ${S}^{1}\ifmmode\times\else\texttimes\fi{}{S}^{2}$ Cauchy surfaces and that satisfies the non-negative-pressures and dominant-energy conditions. Further, an explicit bound is obtained that is determined by the initial data for the spacetime on any Cauchy surface. The conjecture is further studied for the spherically symmetric spacetimes possessing an extra spatial symmetry---the Kantowski-Sachs spacetimes. It is proven, for example, that there exists an upper bound to the lengths of timelike curves in any Kantowski-Sachs spacetime that possesses compact Cauchy surfaces and that satisfies the non-negative-sum-pressures condition.

Bianchi type III and Kantowski-Sachs cosmological models in Lyra geometry

Cosmological models for Bianchi type III and Kantowski-Sachs space-times within the framework of Lyra geometry are obtained. The physical behavior of the models is also discussed.

Quantum wormholes in Kantowski-Sachs spacetime

Asymptotically R 3×S 1 and R 2×S 2 quantum wormholes studied in a Kantowski-Sachs spacetime minimally coupled to a massless scalar field. For this minisuperspace model, two different families of wave functions are found which satisfy the extension to this case of the Hawking boundary conditions for wormholes. They both are linear combinations of another set of solutions of the Wheeler-DeWitt equation which show evidence of a wormhole throat with scalar flux through it. One of these families is given in terms of harmonic oscillator wave functions and depends, as well, on an additional continuous parameter. There is only one wave function which is asymptotically R 2×S 2 and corresponds to pure gravity.

Perfect fluids and Ashtekar variables, with applications to Kantowski-Sachs models

Starting from a variational principle for perfect fluids, the authors develop a Hamiltonian formulation for perfect fluids coupled to gravity expressed in Ashtekar's spinorial variables. The constraint and evolution equations for the gravitational variables are at most quadratic in these variables, as in the vacuum case and in the coupling of gravity to other matter fields, while some of the matter evolution equations are in general non-polynomial. They specialize the formalism to barotropic fluids and spherically symmetric spacetimes, and, within this class, to Kantowski-Sachs spacetimes. They find explicitly the Kantowski-Sachs solutions corresponding to 'stiff matter', which they use as examples to look at the behaviour of the Ashtekar variables when the spatial metric becomes degenerate on one hypersurface. They find that in these solutions the coordinate time arising in the present treatment is singularly related to proper time, and the singularities are only reached at infinite values of the former. They obtain some simple necessary conditions that have to be satisfied if one wants to evolve data past singularities of this kind. None of the barotropic-fluid-filled Kantowski-Sachs spacetimes satisfy these conditions.

Note on Kantowski-Sachs spacetimes

It is shown that a portion of de Sitter space can be expressed in the formds 2=dt 2−A 2 (t)dr 2−B 2(t)(dθ 2+sin 2 θdφ 2). It follows that it is a Kantowski-Sachs spacetime, according to the usual definition. This disproves the statement sometimes seen in the literature that all Kantowski-Sachs spacetimes are anisotropic.

Exact Bianchi-Kantowski-Sachs solutions of Einstein's field equations

The author presents some old and many new exact solutions of the Einstein-Maxwell equations for the Bianchi type-III and Kantowski-Sachs space-times in a unique parametrisation. Solutions are given for the case of stiff matter and dust with (and without) a cosmological constant.

Approximate symmetry groups of inhomogeneous metrics: Examples

By definition, an N-dimensional positive-definite inhomogeneous metric is not invariant under any N-parameter, simply-transitive continuous group of motions. Nonetheless, it is possible to construct a group (simply-transitive and of N parameters) that comes closest to leaving the given metric invariant. We call this group the approximate symmetry group of the metric. In an earlier paper, we described a technique for constructing the approximate symmetry group of a given metric. Here, we briefly review that technique and then present some examples of its application. All two-dimensional metrics are analyzed, and simple criteria are given for determining their approximate symmetry groups. Three three-dimensional metrics are investigated: the invariant hypersurfaces of the Kantowski–Sachs space–times and two families of hypersurfaces in the Gowdy T3 space–times. The approximate symmetry group of the former is found to be of Bianchi Type I and those of the latter may be I or VI0. Defining, via our technique, a measure I of the magnitude of a metric’s inhomogeneity, we study the time dependence of I for the hypersurfaces in the Gowdy metric. We find it is possible in some cases for these hypersurfaces to approach homogeneity (I→0) both in the asymptotic future and near the initial singularity. Finally, we constant a homogeneous background metric for these hypersurfaces.