Topological Censorship

Details Topological Censorship Topological Censorship

1993-05-23

arxiv.org/abs/gr-qc/9305017v2

Phys.Rev.Lett. 71 (1993) 1486-1489; Erratum-ibid. 75 (1995) 1872

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, REVTEX; 1 postscript figure in a separate uuencoded file. Our earlier version (PRL 71, 1486 (1993)) contained a seco

Scientific paper

10.1103/PhysRevLett.75.1872

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).

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