Topological Censorship

TL;DR

This paper proves that in certain physically realistic spacetimes, the topology cannot be observed by causal signals because it collapses too quickly, effectively hiding the topology from any observer.

Contribution

It establishes a topological censorship theorem in general relativity, showing that the topology of spacetime cannot be probed by causal curves under specific conditions.

Findings

Causal curves are homotopic to trivial curves in the specified spacetimes.

The theorem applies to asymptotically flat, globally hyperbolic spacetimes satisfying the null energy condition.

Topological structures are hidden from observers due to rapid collapse.

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 Poincar\'e conjecture is false, the theorem does not prevent one from probing fake 3-spheres).