2008/10/31 by E. Minguzzi · 1 citation
Physics and Astronomy · #gr-qc
paper · pdf · doi:10.1016/j.geomphys.2009.03.007
published as J. Geom. Phys.59:827-833, 2009 · 14 pages, 2 figure. v2: Added material on global hyperbolicity. The title has changed. Previous title: Characterization of causal simplicity and causal continuity through the continuity of the Lorentzian distance. v3: Some misprints fixed. Final version
arxiv created 2009/04/18 · arxiv updated 2011/06/24
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.