Instability of Closed Spaces in General Relativity

Deser, Stanley; Brill, D.

doi:10.1007/BF01645610

Instability of Closed Spaces in General Relativity

1973

Published in:

Commun.Math.Phys. 32 (1973) 291

DOI:

10.1007/BF01645610

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Abstract: (Springer)

There are strong restrictions on the solutions of the initial value constraints of General Relativity when the spatial hypersurface is closed. In particular, closed flat space is unstable: not all solutions of the linearized constraints correspond to nearby solutions of the constraints themselves. For example, no nearby solutions whatever exist which are time symmetric. Other restrictions, which limit perturbations of non-flat closed initial solutions, are also exhibited.

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