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Geodesic focusing and space-time topology

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Abstract

Given a space-timeM and a pointp inM, it is shown that, if the locus of first conjugate points ofp along future-directed null geodesics consists of a single point, thenM admits a compact (S 3) spacelike hypersurface. If in addition the null geodesics do not intersect before focusing, then, in a simply connected space-time, the spacelike hypersurface is a partial Cauchy surface.

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References

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  • Rosquist, K. (1982). “Isotropic Focusing of Light Rays in Cosmology” (to appear inGeneral Relativity and Gravitation).

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Authors and Affiliations

  1. Institute of Theoretical Physics, University of Stockholm, Stockholm, Sweden

    Kjell Rosquist

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  1. Kjell Rosquist
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Rosquist, K. Geodesic focusing and space-time topology. Int J Theor Phys 22, 971–979 (1983). https://doi.org/10.1007/BF02080546

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  • DOI: https://doi.org/10.1007/BF02080546

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