GRG Editor's Choice: Causal geodesic incompleteness of spacetimes arising from IMP gluing

Burkhart, M. & Pollack, D., Causal geodesic incompleteness of spacetimes arising from IMP gluing, Gen Relativ Gravit (2019) 51: 139. https://doi.org/10.1007/s10714-019-2621-3

Editor's Choice (Research Article)

First Online: 29 October 2019

"The main result of the paper establishes that the evolution of initial data sets produced by a well-established connected-sum gluing procedure must be null geodesically incomplete. The work employs a recent lemma due to Galloway–Ling, and the work complements nicely the recent work of the authors (joint w. M. Lesourd). The result of the paper is interesting and timely."

Abstract:

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.

The authors: 

Madeleine J. Burkhart is a Graduate Student under the supervision of Prof. Daniel Pollack in the Department of Mathematics at the University of Washington, Seattle, USA.  Pollack's fields of interest are Differential Geometry, General Relativity, and Partial Differential Equations.

GRG Editor's Choice:

In each volume of GRG, a few papers are marked as “Editor’s Choice”. The primary criteria is original, high quality research that is of wide interest within the community.