Topology and incompleteness for 2+1-dimensional cosmological spacetimes

Author(s)
David Fajman
Abstract

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.

Organisation(s)
Gravitational Physics
Journal
Letters in Mathematical Physics
Volume
107
Pages
1157-1176
No. of pages
20
ISSN
0377-9017
DOI
https://doi.org/10.1007/s11005-016-0932-9
Publication date
06-2017
Peer reviewed
Yes
Austrian Fields of Science 2012
103028 Theory of relativity, 103019 Mathematical physics
Keywords
ASJC Scopus subject areas
Statistical and Nonlinear Physics, Mathematical Physics
Portal url
https://ucrisportal.univie.ac.at/en/publications/topology-and-incompleteness-for-21dimensional-cosmological-spacetimes(6b19f872-0e75-4cc0-8270-a43beb32d97e).html