Abstract
We prove the existence for an infinite proper time in the expanding direction of spacetimes satisfying the vacuum Einstein equations on a manifold of the form \( \sum { \times {S^1} \times R}\) where Σ is a compact surface of genus G >1. The Cauchy data are supposed to be invariant with respect to the group S1 and sufficiently small, but we do not impose a restrictive hypothesis made in the previous work [1]
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References
Y. Choquet-Bruhat and V. MoncriefFuture global einsteinian spacetimes with U(1) isometry groupC.R. Acad. Sci. Paris t. 332 serieI(2001), 137–144; Ann.H.Poincaré2(2001), 1007–1064.
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L. Andersson, V. Moncrief and A. TrombaOn the global evolution problem in 2+1 gravityJ. Geom. Phys.23no. 3–4 (1997), (1991), 205.
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Choquet-Bruhat, Y., Moncrief, V. (2003). Nonlinear Stability of an Expanding Universe with the S 1 Isometry Group. In: Kajitani, K., Vaillant, J. (eds) Partial Differential Equations and Mathematical Physics. Progress in Nonlinear Differential Equations and Their Applications, vol 52. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0011-6_5
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DOI: https://doi.org/10.1007/978-1-4612-0011-6_5
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6572-6
Online ISBN: 978-1-4612-0011-6
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