Isocausal spacetimes may have different causal boundaries

TL;DR

The paper demonstrates that two isocausal spacetimes can have different causal boundaries, highlighting limitations in the invariance of the c-boundary under isocausality and suggesting new avenues for understanding and computing causal boundaries.

Contribution

It provides a specific example showing that isocausality does not guarantee identical c-boundaries, revealing a nuanced aspect of spacetime causal structure.

Findings

Isocausal spacetimes can have non-equivalent c-boundaries.

The example illustrates limitations of isocausality in preserving causal boundary structures.

Suggests isocausality may aid in understanding and computing c-boundaries.

Abstract

We construct an example which shows that two isocausal spacetimes, in the sense introduced by Garc\'ia-Parrado and Senovilla, may have c-boundaries which are not equal (more precisely, not equivalent, as no bijection between the completions can preserve all the binary relations induced by causality). This example also suggests that isocausality can be useful for the understanding and computation of the c-boundary.