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On the Topology and Future Stability of the Universe$
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Hans Ringström

Print publication date: 2013

Print ISBN-13: 9780199680290

Published to Oxford Scholarship Online: September 2013

DOI: 10.1093/acprof:oso/9780199680290.001.0001

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The initial value problem

The initial value problem

Chapter:
(p.369) 22 The initial value problem
Source:
On the Topology and Future Stability of the Universe
Author(s):

Hans Ringström

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199680290.003.0022

In Chapter 22, we turn to the geometric formulation of the initial value problem for the Einstein–Vlasov equations. In particular, we prove, given initial data, that there is a globally hyperbolic development. Moreover, we prove that two globally hyperbolic developments of the same data are extensions of a common globally hyperbolic development of the initial data. The last statement can be interpreted as a geometric version of local uniqueness.

Keywords:   initial value problem, globally hyperbolic development, geometric uniqueness, einstein–vlasov equations

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