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On null cut points in two-dimensional spacetimes. (English) Zbl 1283.53023

Conjugate points and cut points play an important role in singularity theory and causality theory.
There are no null conjugate points in two-dimensional space-times, however, there exists a two-dimensional space-time in which every null geodesic has cut points. This space-time has compact Cauchy surfaces.
In the paper it is shown that for two-dimensional Lorentzian manifolds with noncompact Cauchy surfaces there exist no cut points along null geodesics.

MSC:

53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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