Topological Censorship

TL;DR

It is shown that the topology of physically reasonable isolated systems is shrouded from distant observers, or in other words there is a topological censorship principle.

Abstract

All three-manifolds are known to occur as Cauchy surfaces of asymptotically flat vacuum spacetimes and of spacetimes with positive-energy sources. We prove here the conjecture that general relativity does not allow an observer to probe the topology of spacetime: any topological structure collapses too quickly to allow light to traverse it. More precisely, in a globally hyperbolic, asymptotically flat spacetime satisfying the null energy condition, every causal curve from $\scri^-$ to ${\scri}^+$ is homotopic to a topologically trivial curve from $\scri^-$ to ${\scri}^+$. (If the Poincaré conjecture is false, the theorem does not prevent one from probing fake 3-spheres).

Figures (1)

• Figure 1: The Penrose diagram for an $RP^3$ geon. Each point in the diagram is a two-sphere except for the left vertical boundary, whose points are $RP^2$'s.