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Journal Article

Dynamics of solutions of the Einstein equations with twisted Gowdy symmetry


Rendall,  Alan D.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Rendall, A. D. (2012). Dynamics of solutions of the Einstein equations with twisted Gowdy symmetry. Journal of Geometry and Physics, 62(3), 569-577. doi:10.1016/j.geomphys.2011.04.016.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-D164-D
Some of the most interesting results on the global dynamics of solutions of the vacuum Einstein equations concern the Gowdy spacetimes whose spatial topology is that of a three-dimensional torus. In this paper certain of these ideas are extended to a wider class of vacuum spacetimes where the spatial topology is that of a non-trivial torus bundle over a circle. Compared to the case of the torus these are topologically twisted. They include inhomogeneous generalizations of the spatially homogeneous vacuum spacetimes of Bianchi types II and VI${}_0$. Using similar procedures it is shown that the vacuum solutions of Bianchi type VII${}_0$ are isometric to a class of Gowdy spacetimes, the circular loop spacetimes, thus establishing links between results in the literature which were not previously known to be related to each other.