Topological censorship

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 ${\mathit{scrI}}^{\mathrm{\ensuremath{-}}}$ to ${\mathit{scrI}}^{+}$ is homotopic to a topologically trivial curve from ${\mathit{scrI}}^{\mathrm{\ensuremath{-}}}$ to ${\mathit{scrI}}^{+}$.