Symmetries of cosmological Cauchy horizons

@article{Moncrief1983SymmetriesOC,
  title={Symmetries of cosmological Cauchy horizons},
  author={Vincent Moncrief and James Allen Isenberg},
  journal={Communications in Mathematical Physics},
  year={1983},
  volume={89},
  pages={387-413}
}
We consider analytic vacuum and electrovacuum spacetimes which contain a compact null hypersurface ruled byclosed null generators. We prove that each such spacetime has a non-trivial Killing symmetry. We distinguish two classes of null surfaces, degenerate and non-degenerate ones, characterized by the zero or non-zero value of a constant analogous to the “surface gravity” of stationary black holes. We show that the non-degenerate null surfaces are always Cauchy horizons across which the Killing… 
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References

SHOWING 1-6 OF 6 REFERENCES
The Large Scale Structure of Space-Time
TLDR
The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions.
Infinite Dimensional Family of Vacuum Cosmological Models With Taub - {NUT} (Newman-Unti-Tamburino) Type Extensions
We show that the Gowdy metrics on T/sup 3/ x R contain an infinite-dimensional subfamily of solutions which each admit a Taub-NUT (Newman-Unti-Tamburino)-type extension. However we also show that the
The structure of the space of solutions of Einstein's equations. I. One Killing field.
This paper deals with globally hyperbolic solutions of the vacuum Einstein equations in a neighborhood of spacetimes that have a compact Cauchy surface of constant mean curvature. The first part of
General Relativity; an Einstein Centenary Survey
List of contributors Preface 1. An introductory survey S. W. Hawking and W. Israel 2. The confrontation between gravitation theory and experiment C. M. Will 3. Gravitational-radiation experiments D.