Neighborhoods of Cauchy horizons in cosmological spacetimes with one killing field
In this paper we show how to construct an infinite dimensional family of analytic, vacuum spacetimes which each have (i) T/sup 3/ x R topology, (ii) a smooth, compact Cauchy horizon, and (iii) a single Killing vector field which is spacelike in the globally hyperbolic region, null on the horizon and timelike in the (acausal) extension. The key idea is to use the horizons themselves as initial data surfaces and to prove the local existence of solutions using a version of the Cauchy-Kowalewski theorem. Factoring by the action of analytic, horizon preserving diffeomorphisms we define a ''space of extendible vacuum spacetimes'' of the given symmetry type and show (modulo certain smoothness estimates which we do not attempt to derive) that this space defines a Lagrangian submanifold of the usual phase space for Einstein's equations. We also study the linear perturbations of a class of the extendible spacetimes and show that the generic such perturbation blows up near the background solution's Cauchy horizon. This result, though limited by the linearity of the approximation, conforms to the usual picture of unstable Cauchy horizons demanded by the strong cosmic censorship conjecture.
- Research Organization:
- Department of Physics, Yale University, New Haven, Connecticut 06511
- OSTI ID:
- 5031493
- Journal Information:
- Ann. Phys. (N.Y.); (United States), Vol. 141:1
- Country of Publication:
- United States
- Language:
- English
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