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 is a spacetime with timelike boundary , where is diffeomorphic to , and that for each , is spacelike. He further assumes that for each , the null second fundamental forms corresponding to (any) inward (respectively, outward) pointing null vector field are negative (respectively, positive) definite. Each is supposed to be acausal in and the null convergence condition is assumed to hold. Under these conditions, global hyperbolicity of implies that this set is simply connected.
In the asymptotically flat case, there exist timelike tubes near infinity which satisfy the assumptions above and the theorem can be applied to the complement of the asymptotic region bounded by .
He also shows that if the boundary of consists of several timelike tubes and is globally hyperbolic, then , provided . A possible interpretation of this theorem is that in globally hyperbolic spacetimes there are no wormholes connecting different asymptotic regions.