Thurston's geometrization conjecture and cosmological models

Katsuhito Yasuno, Tatsuhiko Koike, Masaru Siino

研究成果: Article査読

3 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1405-1420
ページ数16
ジャーナルClassical and Quantum Gravity
18
8
DOI
出版ステータスPublished - 2001 4 21

ASJC Scopus subject areas

  • 物理学および天文学(その他)

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