Isocausal spacetimes may have different causal boundaries

We construct an example which shows that two isocausal spacetimes, in the sense introduced recently in Garcia-Parrado and Senovilla (2003 Class. Quantum Grav. 20 625-64), 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.