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A ‘finite infinity’ version of topological censorship. (English) Zbl 0853.53069

The author gives a version of the topological censorship theorem of J. L. Friedmann, K. Schleich and D. M. Witt [Phys. Rev. Lett. 71, 1486-1489 (1993)] without the assumption of asymptotic flatness. He assumes that (M,g) is a spacetime with timelike boundary M=T, where T is diffeomorphic to ×S 2 , and that for each t, Σ t :={t}×S 2 is spacelike. He further assumes that for each Σ t , the null second fundamental forms corresponding to (any) inward (respectively, outward) pointing null vector field are negative (respectively, positive) definite. Each Σ t is supposed to be acausal in M and the null convergence condition is assumed to hold. Under these conditions, global hyperbolicity of J + (T)J - (T) implies that this set is simply connected.

In the asymptotically flat case, there exist timelike tubes T near infinity which satisfy the assumptions above and the theorem can be applied to the complement of the asymptotic region bounded by T.

He also shows that if the boundary of M consists of several timelike tubes {T α } α and (M,g) is globally hyperbolic, then J + (T a )J - (T b )=, provided ab. A possible interpretation of this theorem is that in globally hyperbolic spacetimes there are no wormholes connecting different asymptotic regions.

MSC:
53Z05Applications of differential geometry to physics
83C75Space-time singularities, cosmic censorship, etc.