id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
work_5uxr4kcusfhdrhcn3j6ouxq3nu	John Byron Manchak	On Space-Time Singularities, Holes, and Extensions	2014	10	.pdf	application/pdf	4183	445	72	In what follows, we consider three spacetime conditions of interest: geodesic reasonable spacetimes while hole-freeness and inextendibility are usually taken to be satisfied time orientable spacetime allows one to distinguish between the future and past D−(S), to be the set of points p ∈ M such that every causal curve with past endpoint p and no future endpoint intersects S. Definition 3.1 A spacetime (M,gab) is geodesically complete (GC) if every Of course, there are also a large number of geodesically incomplete spacetimes which seem to have "artificial" singularities. any spacetime with one point removed from the manifold is geodesically incomplete. Definition 3.3 A spacetime (M,gab) is hole-free (HF) if, for every set K ⊆ M intermediate conditions: one between geodesic completeness and hole-freeness geodesic completeness and implies both hole-freeness and inextendibility? future or past incomplete timelike geodesic γ : I → M, and every open set O	./cache/work_5uxr4kcusfhdrhcn3j6ouxq3nu.pdf	./txt/work_5uxr4kcusfhdrhcn3j6ouxq3nu.txt