Isocausal spacetimes may have different causal boundaries

Abstract

We construct an example which shows that two isocausal spacetimes, in the sense introduced by García-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.

Minor modifications, including the title, which matches now with the published version. 12 pages, 3 figures

References in corpus (5)

• The Causal Boundary of spacetimes revisited
• The causal boundary of wave-type spacetimes
• Topology of the Causal Boundary for Standard Static Spacetimes
• The causal boundary of product spacetimes
• Causal boundaries and holography on wave type spacetimes

Cited by in corpus (5)

• The 1965 Penrose singularity theorem
• Globally hyperbolic spacetimes: slicings, boundaries and counterexamples
• Hausdorff separability of the boundaries for spacetimes and sequential spaces
• Computability of the causal boundary by using isocausality
• The Strongly Attached Point Topology of the Abstract Boundary For Space-Time