TY - JOUR
T1 - Topology and incompleteness for 2+1-dimensional cosmological spacetimes
AU - Fajman, David
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media Dordrecht.
PY - 2017/6
Y1 - 2017/6
N2 - We study the long-time behavior of the Einstein flow coupled to matter on 2-dimensional surfaces. We consider massless matter models such as collisionless matter composed of massless particles, massless scalar fields and radiation fluids and show that the maximal globally hyperbolic development of homogeneous and isotropic initial data on the 2-sphere is geodesically incomplete in both time directions, i.e. the spacetime recollapses. This behavior also holds for open sets of initial data. In particular, we construct classes of recollapsing 2+1-dimensional spacetimes with spherical spatial topology which provide evidence for a closed universe recollapse conjecture for massless matter models in 2+1 dimensions. Furthermore, we construct solutions with toroidal and higher genus topology for the massless matter fields, which in both cases are future complete. The spacetimes with toroidal topology are 2+1-dimensional analogies of the Einstein–de Sitter model. In addition, we point out a general relation between the energy-momentum tensor and the Kretschmann scalar in 2+1 dimensions and use it to infer strong cosmic censorship for all these models. In view of this relation, we also recall corresponding models containing massive particles, constructed in a previous work and determine the nature of their initial singularities. We conclude that the global structure of non-vacuum cosmological spacetimes in 2+1 dimensions is determined by the mass of particles and—in the homogeneous and isotropic setting studied here—verifies strong cosmic censorship.
AB - We study the long-time behavior of the Einstein flow coupled to matter on 2-dimensional surfaces. We consider massless matter models such as collisionless matter composed of massless particles, massless scalar fields and radiation fluids and show that the maximal globally hyperbolic development of homogeneous and isotropic initial data on the 2-sphere is geodesically incomplete in both time directions, i.e. the spacetime recollapses. This behavior also holds for open sets of initial data. In particular, we construct classes of recollapsing 2+1-dimensional spacetimes with spherical spatial topology which provide evidence for a closed universe recollapse conjecture for massless matter models in 2+1 dimensions. Furthermore, we construct solutions with toroidal and higher genus topology for the massless matter fields, which in both cases are future complete. The spacetimes with toroidal topology are 2+1-dimensional analogies of the Einstein–de Sitter model. In addition, we point out a general relation between the energy-momentum tensor and the Kretschmann scalar in 2+1 dimensions and use it to infer strong cosmic censorship for all these models. In view of this relation, we also recall corresponding models containing massive particles, constructed in a previous work and determine the nature of their initial singularities. We conclude that the global structure of non-vacuum cosmological spacetimes in 2+1 dimensions is determined by the mass of particles and—in the homogeneous and isotropic setting studied here—verifies strong cosmic censorship.
KW - Einstein-Vlasov system
KW - Massless particles
KW - 2+1-Dimensional general relativity
KW - Closed universe recollapse
KW - Strong cosmic censorship
KW - UNIVERSE RECOLLAPSE CONJECTURE
KW - HYPERBOLIC SYMMETRY
KW - GENERAL-RELATIVITY
KW - EINSTEIN EQUATIONS
KW - EVOLUTION
KW - SYSTEM
KW - REDUCTION
KW - EXISTENCE
KW - PLANE
KW - TIMES
KW - Einstein–Vlasov system
UR - http://www.scopus.com/inward/record.url?scp=85006914584&partnerID=8YFLogxK
U2 - 10.1007/s11005-016-0932-9
DO - 10.1007/s11005-016-0932-9
M3 - Article
SN - 0377-9017
VL - 107
SP - 1157
EP - 1176
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
IS - 6
ER -