A note on causally simple and globally hyperbolic spacetimes
نویسنده
چکیده
Given an arbitrary spacetime (M, g), we prove a simple criterion to check when many of the good properties of the time-separation (Lorentzian distance) d valid in globally hyperbolic spacetimes hold for M . Concretely, when the product P = M × R, g̃ = g + dy is causally simple, then not only M is causally simple, but also d is continuous and AvezSeifert connectedness (each two causally related events x, z ∈ M with d(x, z) < ∞ can be joined by a length maximizing causal geodesic) holds. We also remark that the used characterization of causal simplicity also simplifies the definition of global hyperbolicity. 2000 MSC: Primary 53C50, Secondary 53C80, 83C75.
منابع مشابه
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