Geroch's theorem states that if two spacelike hypersurfaces lie in hole-free spacetimes and an isometry exists between those spacetimes, then the isometry extends to an isometry between the future domains of dependence of those hypersurfaces.
Hole-free spacetimes(as used in general relativity)
Models of the universe (in Einstein's theory) that don't have gaps or missing regions where the laws of physics break down.
Isometry(as used in geometry and physics)
A mathematical transformation that preserves distances and shapes—think of it like rotating or reflecting an object without stretching or squishing it.
spacelike hypersurfaces(Relativistic cosmology)
Surfaces of simultaneity defined with respect to cosmic time x^0, representing spatial slices of spacetime at a given cosmic time
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