TY - JOUR

T1 - Topology and Singularities in Cosmological Spacetimes Obeying the Null Energy Condition

AU - Galloway, Gregory J.

AU - Ling, Eric

N1 - Funding Information:
Research partially supported by NSF Grant DMS-1313724.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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 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.

AB - 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 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.

UR - http://www.scopus.com/inward/record.url?scp=85033481744&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85033481744&partnerID=8YFLogxK

U2 - 10.1007/s00220-017-3020-9

DO - 10.1007/s00220-017-3020-9

M3 - Article

AN - SCOPUS:85033481744

VL - 360

SP - 611

EP - 617

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -