The causal automorphism of de Sitter and Einstein cylinder spacetimes

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Abstract
A well-known result, due originally to Alexandrov in 1953 and subsequently rediscovered by Zeeman in 1964, states that transformations of Minkowski spacetime which preserve causality are essentially orthochronous Lorentz transformations. In this article, we first exhibit a proof of this result by using a lemma of Zeeman to reduce the proof to another well-known theorem of Alexandrov involving transformations preserving light speed. Then, by generalizing Zeeman’s lemma and using recent extensions of Alexandrov’s light-speed theorem, we determine the causal automorphisms of de Sitter and Einstein cylinder spacetimes.

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