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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

(p.369) 22 The initial value problem
On the Topology and Future Stability of the Universe

Hans Ringström

Oxford University Press

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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