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Zbl 0853.53069
Galloway, Gregory J.
A `finite infinity' version of topological censorship. (English)
[J] Classical Quantum Gravity 13, No.6, 1471-1478 (1996). ISSN 0264-9381; ISSN 1361-6382/e

The author gives a version of the topological censorship theorem of {\it J. L. Friedmann}, {\it K. Schleich} and {\it 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 $\partial M=T$, where $T$ is diffeomorphic to $\bbfR \times S^2$, and that for each $t$, $\Sigma_t:= \{t \}\times S^2$ is spacelike. He further assumes that for each $\Sigma_t$, the null second fundamental forms corresponding to (any) inward (respectively, outward) pointing null vector field are negative (respectively, positive) definite. Each $\Sigma_t$ is supposed to be acausal in $M$ and the null convergence condition is assumed to hold. Under these conditions, global hyperbolicity of $J^+ (T)\cap J^- (T)$ implies that this set is simply connected. \par 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 $T$. \par He also shows that if the boundary of $M$ consists of several timelike tubes $\{T_\alpha \}_\alpha$ and $(M, g)$ is globally hyperbolic, then $J^+ (T_a) \cap J^- (T_b)= \emptyset$, provided $a\ne b$. A possible interpretation of this theorem is that in globally hyperbolic spacetimes there are no wormholes connecting different asymptotic regions.
[M.Kriele (Berlin)]

MSC 2000:: *53Z05 Appl. of differential geometry to physics
83C75 Space-time singularities, etc.

Keywords: topological consorship; causal methods; energy condition; outer communication; infinity

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