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On Level Sets of Lorentzian Distance Function

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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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Authors and Affiliations

  1. Department of Mathematics, Hacettepe University, Beytepe, 06532, Ankara, Turkey

    F. Erkekoğlu

  2. Department of Geometry and Topology, Faculty of Mathematics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    E. García-Río

  3. Bosna-Hersek Caddesi, No: 35/B-10, Emek Mahallesi, 06510, Ankara, Turkey

    D. N. Kupeli

Authors
  1. F. Erkekoğlu
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  2. E. García-Río
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  3. D. N. Kupeli
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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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  • DOI: https://doi.org/10.1023/A:1025779017980

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