The problem of existence of timelike or null geodetic arcs is examinated. It is shown that some transparent causality conditions are sufficient for the existence of an extremal geodetic arc between every pair of events joined by a timelike curve. In the case of a complete space-time these assumptions are also necessary. Some applications to the existence of global space-sections and the structure of space-times with a Cauchy surface are given.
Received: 1967-6-5
Published Online: 2014-6-2
Published in Print: 1967-9-1
© 1946 – 2014: Verlag der Zeitschrift für Naturforschung
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