# Causal geodesic incompleteness of spacetimes arising from IMP gluing

## TL;DR

This paper analyzes the local geometry of IMP gluing initial data sets and demonstrates that their spacetime developments are null geodesically incomplete, extending Penrose's incompleteness theorem.

## Contribution

It establishes conditions for outer trapped surfaces in IMP glued data and proves null incompleteness of the resulting spacetimes.

## Key findings

- Existence of outer trapped surfaces near the gluing neck
- Null geodesic incompleteness of the constructed spacetimes
- Application of a generalized Penrose theorem

## Abstract

In 2002, Isenberg-Mazzeo-Pollack (IMP) constructed a series 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.