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In this article, we extend a construction of Chruściel et al. (Commun Math Phys 257(1):29–42, 2005) to obtain a large class of vacuum cosmological spacetimes that do not contain any CMC Cauchy surfaces. The allowed spatial topologies for these examples are of the form \(M \# M\) , where M is any closed, connected, oriented, irreducible 3-manifold which is not spherical. This complements the recent results of Ling and Ohanyan (Lett Math Phys 114(4):96, 2024), where, instead of initial data methods, global spacetime gluing arguments were used. The study of such examples is sure to yield insight into Bartnik’s cosmological splitting conjecture (Bartnik, Commun Math Phys 117(4):615–624, 1988).

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Vacuum Cosmological Spacetimes Without CMC Cauchy Surfaces

  • 会议论文

  • 发表日期：

    2025年

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  • Eric Ling,
  • Argam Ohanyan

摘要

In this article, we extend a construction of Chruściel et al. (Commun Math Phys 257(1):29–42, 2005) to obtain a large class of vacuum cosmological spacetimes that do not contain any CMC Cauchy surfaces. The allowed spatial topologies for these examples are of the form \(M \# M\) , where M is any closed, connected, oriented, irreducible 3-manifold which is not spherical. This complements the recent results of Ling and Ohanyan (Lett Math Phys 114(4):96, 2024), where, instead of initial data methods, global spacetime gluing arguments were used. The study of such examples is sure to yield insight into Bartnik’s cosmological splitting conjecture (Bartnik, Commun Math Phys 117(4):615–624, 1988).