Topology and Singularities in Cosmological Spacetimes Obeying the Null Energy Condition

2017/05/31 by Gregory J. Galloway, Eric Ling · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cauchy distribution #Combinatorics #Computer science #Connection (principal bundle) #Cosmological constant #Cosmology and Gravitation Theories #Energy condition #General relativity #Geometric Analysis and Curvature Flows #Geometry #Gravitational singularity #Mathematical analysis #Mathematical physics #Mathematics #Null (SQL) #Physics #Pure mathematics #Singularity #Topology (electrical circuits) #gr-qc #math.DG

paper · pdf · doi:10.1007/s00220-017-3020-9

8 pages; v2: minor changes, version to appear in CMP

openalex created_date 2017/05/26 · openalex publication_date 2017/11/09 · arxiv created 2018/03/09 · arxiv updated 2018/03/13 · openalex updated_date 2026/08/05

Abstract

We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3+1 dimensional spacetimes which satisfy the null energy condition and contain a future expanding compact Cauchy surface, we establish a precise connection between the topology of the Cauchy surfaces and the occurrence of past singularities. In addition to (a refinement of) the Penrose singularity theorem, the proof makes use of some recent advances in the topology of 3-manifolds and of certain fundamental existence results for minimal surfaces.

Citations

• The Large Scale Structure of Space-Time
• Immersing almost geodesic surfaces in a closed hyperbolic three manifold
• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

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• The Big Bang is a Coordinate Singularity for k = -1 Inflationary FLRW Spacetimes