### Abstract

We investigate a class of spatially compact inhomogeneous spacetimes. Motivated by Thurston's geometrization conjecture, we give a formulation for constructing spatially compact composite spacetimes as solutions for the Einstein equations. Such composite spacetimes are built from the spatially compact locally homogeneous vacuum spacetimes which have two commuting local Killing vector fields and are homeomorphic to torus bundles over the circle by gluing them through a timelike hypersurface admitting a homogeneous spatial torus spanned by the commuting local Killing vector fields. We also assume that the matter which will arise from the gluing is compressed on the boundary, i.e. we take the thin-shell approximation. By solving the junction conditions, we can see dynamical behaviour of the connected (composite) spacetime. The Teichmüller deformation of the torus can also be obtained. We apply our formalism to a concrete model. The relation to the torus sum of 3-manifolds and the difficulty of this problem are also discussed.

Original language | English |
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Pages (from-to) | 1405-1420 |

Number of pages | 16 |

Journal | Classical and Quantum Gravity |

Volume | 18 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2001 Apr 21 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Classical and Quantum Gravity*,

*18*(8), 1405-1420. https://doi.org/10.1088/0264-9381/18/8/301

**Thurston's geometrization conjecture and cosmological models.** / Yasuno, Katsuhito; Koike, Tatsuhiko; Siino, Masaru.

Research output: Contribution to journal › Article

*Classical and Quantum Gravity*, vol. 18, no. 8, pp. 1405-1420. https://doi.org/10.1088/0264-9381/18/8/301

}

TY - JOUR

T1 - Thurston's geometrization conjecture and cosmological models

AU - Yasuno, Katsuhito

AU - Koike, Tatsuhiko

AU - Siino, Masaru

PY - 2001/4/21

Y1 - 2001/4/21

N2 - We investigate a class of spatially compact inhomogeneous spacetimes. Motivated by Thurston's geometrization conjecture, we give a formulation for constructing spatially compact composite spacetimes as solutions for the Einstein equations. Such composite spacetimes are built from the spatially compact locally homogeneous vacuum spacetimes which have two commuting local Killing vector fields and are homeomorphic to torus bundles over the circle by gluing them through a timelike hypersurface admitting a homogeneous spatial torus spanned by the commuting local Killing vector fields. We also assume that the matter which will arise from the gluing is compressed on the boundary, i.e. we take the thin-shell approximation. By solving the junction conditions, we can see dynamical behaviour of the connected (composite) spacetime. The Teichmüller deformation of the torus can also be obtained. We apply our formalism to a concrete model. The relation to the torus sum of 3-manifolds and the difficulty of this problem are also discussed.

AB - We investigate a class of spatially compact inhomogeneous spacetimes. Motivated by Thurston's geometrization conjecture, we give a formulation for constructing spatially compact composite spacetimes as solutions for the Einstein equations. Such composite spacetimes are built from the spatially compact locally homogeneous vacuum spacetimes which have two commuting local Killing vector fields and are homeomorphic to torus bundles over the circle by gluing them through a timelike hypersurface admitting a homogeneous spatial torus spanned by the commuting local Killing vector fields. We also assume that the matter which will arise from the gluing is compressed on the boundary, i.e. we take the thin-shell approximation. By solving the junction conditions, we can see dynamical behaviour of the connected (composite) spacetime. The Teichmüller deformation of the torus can also be obtained. We apply our formalism to a concrete model. The relation to the torus sum of 3-manifolds and the difficulty of this problem are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=0035626377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035626377&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/18/8/301

DO - 10.1088/0264-9381/18/8/301

M3 - Article

VL - 18

SP - 1405

EP - 1420

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 8

ER -