arXiv subjects
Publications and source records attributed to J. Isenberg.
We use Fuchsian methods to show that, for any two dimensional manifold $Σ^2$, there is a large family of U(1) symmetric solutions of the vacuum Einstein equations on the manifold $Σ\times S^1 \times \mathbb{R}$, each of which has AVTD behavior in the neighborhood of its singularity.
A combination of qualitative analysis and numerical study indicates that vacuum $T^2$ symmetric spacetimes are, generically, oscillatory.
We discuss various features of the dynamical system determined by the flow of null geodesic generators of Cauchy horizons. Several examples with non--trivial (``chaotic'', ``strange attractors'', etc.) global behaviour are constructed. Those examples are relevant to the ``chronology protection conjecture'', and they show that the occurrence of ``fountains'' is {\em not} a generic feature of Cauchy horizons.