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Causally simple spacetimes and naked singularities (2105.03730v1)
Published 8 May 2021 in gr-qc, math-ph, math.DG, and math.MP
Abstract: In this paper, We prove a conjecture which states that if M is a nakedly singular future boundary or nakedly singular past boundary spacetime, then the space of null geodesics, N, is non-Hausdorff. Also, we show that every two-dimensional strongly causal spacetime M is causally simple if and only if it is null pseudoconvex. As a result, it implies the converse of the conjecture for two-dimension but there are examples that refute it for more dimensions.
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