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arXiv · gr-qc/9305017

Topological Censorship

John L. Friedman·Kristin Schleich·Donald M. Witt
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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).

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John L. Friedman, Kristin Schleich, Donald M. Witt. 1995-06-09. Topological Censorship. https://doi.org/10.1103/physrevlett.75.1872

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