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On future asymptotics of polarized Gowdy Bbb T3-models

Thomas Jurke1

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Gowdy's model of cosmological spacetimes is a much investigated subject in classical and quantum gravity. Depending on spatial topology, re-collapsing as well as expanding models are known. Several analytical tools were used in order to clarify singular behaviour in this class of spacetimes. Here we investigate the structure of a certain subclass, the polarized Gowdy models with spatial Bbb T3-topology, in general. The asymptotics for general solutions of the dynamical equation for one of the gravitational degrees of freedom play a key role while the asymptotic behaviour of the remaining metric function is a result of solving the Hamiltonian constraint equation. Using both, we prove future geodesic completeness in all spacetimes of this type.


PACS

04.20.-q Classical general relativity

02.40.-k Geometry, differential geometry, and topology

MSC

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

35Q05 Euler-Poisson-Darboux equation and generalizations

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 1 (7 January 2003)

Received 9 October 2002

Published 12 December 2002



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