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On Level Sets of Lorentzian Distance Function

Abstract

Level sets of Lorentzian distance functions with respect to a point and with respect to an achronal spacelike hypersurface, are analyzed. Some bounds for the Laplacian of such Lorentzian distance functions are obtained and, in relation to them, some spacetime singularity theorems are given.

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Supported by project BFM2001-3778-C03-01 (Spain).

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Erkekoğlu, F., García-Río, E. & Kupeli, D.N. On Level Sets of Lorentzian Distance Function. General Relativity and Gravitation 35, 1597–1615 (2003). https://doi.org/10.1023/A:1025779017980

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  • Lorentzian distance function
  • Lorentzian index form
  • strong causality
  • globally hyperbolicity
  • spacetime singularity