Causal geodesic incompleteness of spacetimes arising from IMP gluing
In 2002, Isenberg–Mazzeo–Pollack (IMP) constructed a family of vacuum initial data sets via a gluing construction. In this paper, we investigate some local geometry of these initial data sets as well as implications regarding their spacetime developments. In particular, we state conditions for the existence of outer trapped surfaces near the center of the IMP gluing neck and thence use a generalization of the Penrose incompleteness theorem to deduce null incompleteness of the resulting spacetimes.
KeywordsInitial data Gluing Outer trapped surfaces Incompleteness
This work was supported by a grant from the Simons Foundation (279720-DP). Both authors would like to thank Greg Galloway for his many helpful suggestions and to the anonymous referee for their comments, which improved the exposition of the paper.
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