Abstract
The statement of the title is proved. It implies that under physically reasonable conditions, spacetimes which are free from singularities are necessarily stably causal and hence admit a time function. Read as a singularity theorem it states that if there is some form of causality violation on spacetime then either it is the worst possible, namely violation of chronology, or there is a singularity. The analogous result: “Non-totally vicious spacetimes without lightlike rays are globally hyperbolic” is also proved, and its physical consequences are explored.
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Communicated by G.W. Gibbons
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Minguzzi, E. Chronological Spacetimes without Lightlike Lines are Stably Causal. Commun. Math. Phys. 288, 801–819 (2009). https://doi.org/10.1007/s00220-009-0784-6
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DOI: https://doi.org/10.1007/s00220-009-0784-6