Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-10-10
J. Geom. Phys.59:827-833, 2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
14 pages, 2 figure. v2: Added material on global hyperbolicity. The title has changed. Previous title: Characterization of cau
Scientific paper
10.1016/j.geomphys.2009.03.007
A classical result in Lorentzian geometry states that a strongly causal spacetime is globally hyperbolic if and only if the Lorentzian distance is finite valued for every metric choice in the conformal class. It is proven here that a non-total imprisoning spacetime is globally hyperbolic if and only if for every metric choice in the conformal class the Lorentzian distance is continuous. Moreover, it is proven that a non-total imprisoning spacetime is causally simple if and only if for every metric choice in the conformal class the Lorentzian distance is continuous wherever it vanishes. Finally, a strongly causal spacetime is causally continuous if and only if there is at least one metric in the conformal class such that the Lorentzian distance is continuous wherever it vanishes.
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