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Geodesic incompleteness cases

  1. Oct 2, 2012 #1
    Hi all,

    I would like to know if somebody know the cases when we have in the space time manifold (and in general in any manifold) geodesic incompleteness.

    I know that a case can be a singularity in the curvature scalar (or in general, a singularity in any component of the Riemann tensor). Also when we remove a point of our manifold.

    I ignore if when we have a singularity due to a bad selection of coordinates (coordinate singularities), there is geodesic incompleteness. Also ignore more cases.

    Thank you in advance.
  2. jcsd
  3. Oct 2, 2012 #2


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    I think it's not enough to remove a point from an otherwise well-behaved spacetime, because we're typically only interested in cases where the spacetime can't be extended in order to restore geodesic completeness. But for example, you could have a conical singularity, in which case geodesics can't be extended through the point where the singularity occurs, and this can't be fixed by extending the spacetime.
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