Starting from any vacuum solution, one can remove a closed set of points lying to the future of a neighborhood of a spacelike hypersurface and within its future domain of dependence.
A mathematical surface in spacetime where all points on it are space-separated from each other (meaning no signal traveling at light speed or slower could connect them), like a snapshot of the entire universe at one moment in time.
vacuum solution(Einstein argued such solutions are impossible for a static universe if Mach's Principle holds)
A solution to the gravitational field equations in which the energy-momentum tensor T_ij is zero, representing a universe with no mass-energy content
The would-be time machine operator need not capitulate in the face of Krasnikov’s theorem. Recall that the main difficulty in specifying the conditions for the successful operation of Thornian time machines traces to the fact that the standard form of causal determinism does not apply to the production of CTCs. But causal determinism can fail for reasons that have nothing to do with CTCs or other acausal features of relativistic spacetimes, and it seems only fair to ensure that these modes of fa