Thurston's geometrization conjecture and cosmological models

Katsuhito Yasuno, Tatsuhiko Koike, Masaru Siino

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3 Citations (Scopus)

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 languageEnglish
Pages (from-to)1405-1420
Number of pages16
JournalClassical and Quantum Gravity
Volume18
Issue number8
DOIs
Publication statusPublished - 2001 Apr 21

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ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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