In:
International Journal of Modern Physics D, World Scientific Pub Co Pte Ltd, Vol. 10, No. 06 ( 2001-12), p. 825-831
Abstract:
We discuss the phase portrait of the reduced Einstein (3+1)-equations on a compact manifold of Yamabe type -1. We show that the flow for these equations either has a unique fixed point if the underlying manifold M is hyperbolizable or has no fixed points if M is not hyperbolizable. Thus the topology of M is a critical determinant of the phase portrait of the reduced equations. If, additionally, M is rigid, the fixed point is a local attractor, thereby answering an important question regarding the stability of these model universes. In the non-hyperbolizable case, under certain conditions, the reduced Einstein flow predicts that the conformal volume collapses M, in contrast to the physical volume which, as befits an expanding universe, goes to infinity as the coordinate time goes to infinity.
Type of Medium:
Online Resource
ISSN:
0218-2718
,
1793-6594
DOI:
10.1142/S0218271801001852
Language:
English
Publisher:
World Scientific Pub Co Pte Ltd
Publication Date:
2001
SSG:
16,12
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