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The Abstract Boundary singularity theorem was first proven by Ashley andScott. It links the existence of incomplete causal geodesics in stronglycausal, maximally extended spacetimes to the existence of Abstract Boundaryessential singularities, i.e., non-removable singular boundary points. We givetwo generalizations of this theorem: the first to continuous causal curves andthe distinguishing condition, the second to locally Lipschitz curves inmanifolds such that no inextendible locally Lipschitz curve is totallyimprisoned. To do this we extend generalized affine parameters from $C^1$curves to locally Lipschitz curves.

Generalizations of the Abstract Boundary singularity theorem