Initial data sets and the topology of closed three-manifolds in general relativity

Abstract

We discuss the interaction between the matter content of a closed physical space, associated with a generic gravitational configuration (i.e. without symmetries), and the topology of the underlying closed three-manifoldS. We show that, within the context of the conformal approach to the initial-value problem, the presence of enough matter and radiation favours those topologies we expect, on heuristic grounds, to be actually encountered, namely the three-sphere topology, or the (S1×S2)-worm-hole topology. We also argue that such topologies leave, as far as the field equations are concerned, more room to possible gravitational initial data sets.