The causal order on the ambient boundary

TL;DR

This paper investigates the causal structure of the ambient boundary in conformal geometry, demonstrating that the horismos order uniquely aligns with its topology, impacting the understanding of time in this setting.

Contribution

It establishes that the horismos order is the only causal relation compatible with the boundary's topology, clarifying the causal structure of the ambient boundary.

Findings

The ambient boundary's causal relation is uniquely determined as horismos.

The global topology constrains the causal structure.

Implications for the notion of time in conformal geometry.

Abstract

We analyse the causal structure of the ambient boundary, the conformal infinity of the ambient (Poincar\'e) metric. Using topological tools we show that the only causal relation compatible with the global topology of the boundary spacetime is the horismos order. This has important consequences for the notion of time in the conformal geometry of the ambient boundary.