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What is Attractors in Spacetimes and Time Functions about?

We develop a new approach to the existence of time functions on Lorentzian manifolds, based on Conley's work regarding Lyapunov functions for dynamical systems. We recover Hawking's result that a stably causal admits a time function through a more general result giving the existence of a continuous function that is non decreasing along all future directed causal curves, and increasing along such curves that lie outside a special region of the spacetime, called the chain recurrent set, which is empty for stably causal spacetimes. The construction is based on a notion of attractive sets in spacetimes.

Author

Monclair, Daniel

Published

2016

Language

EN