On the dynamics of generators of Cauchy horizons

TL;DR

This paper explores the complex dynamics of null geodesic generators of Cauchy horizons, presenting examples with chaotic behavior to inform the understanding of the chronology protection conjecture.

Contribution

It introduces new examples of Cauchy horizons exhibiting non-trivial, chaotic dynamics, challenging the idea that fountains are a generic feature.

Findings

Examples with chaotic and strange attractor behavior are constructed.

Fountains are shown not to be a generic feature of Cauchy horizons.

The results have implications for the chronology protection conjecture.

Abstract

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.