Pure and Applied Mathematics Quarterly

Volume 15 (2019)

Number 3

Special Issue: In Honor of Robert Bartnik (Part 2 of 2)

Guest Editors: Piotr T. Chruściel, Greg Galloway, Jim Isenberg, Pengzi Miao, Mu-Tao Wang, and Shing-Tung Yau

Null geodesic incompleteness of spacetimes with no CMC Cauchy surfaces

Pages: 839 – 849

DOI: https://dx.doi.org/10.4310/PAMQ.2019.v15.n3.a3


Madeleine Burkhart (University of Washington, Seattle, WA., U.S.A.)

Martin Lesourd (University of Oxford, United Kingdom)

Daniel Pollack (University of Washington, Seattle, WA., U.S.A.)


Using an initial data gluing construction, Chruściel, Isenberg, and Pollack constructed a class of vacuum cosmological spacetimes that do not admit Cauchy surfaces with constant mean curvature. We prove that, for sufficiently large values of the gluing parameter, these examples are both future and past null geodesically incomplete.

2010 Mathematics Subject Classification

Primary 83C75. Secondary 53C21, 53C22, 83C05.

The authors are honored to dedicate this work to Robert Bartnik.

This work was supported by a grant from the Simons Foundation (279720-DP).

Received 27 February 2019

Received revised 21 May 2019

Accepted 3 June 2019

Published 2 January 2020