Does GR really allow superluminal movement? In this video, Michio Kaku says 

"...general theory of relativity, where it is possible, we think, that you might be able to go faster than the speed of light..."

Does GR really allow superluminial movement?
 A: There is a subtle difference between "local" and "global" (or apparent) superluminal travel. Kaku is only correct in the global sense.
Local superluminal travel, in the sense of increasing one's speed to exceed the speed of light, is strictly prohibited as special relativity holds in any sufficiently local frame. 
However, general relativity (with the most vague energy conditions), does allow constructs like wormholes, bridges between areas of space-time. Think of going from NYC to London; normally this takes 8 hours, but lets say you were able to stretch the earth placing london right above NYC and you hoped from NYC to London. To a mere earth dwelling creature, who doesn't see the ``global" stretching, it appears that you travelled instantaneously from NYC to London, travelling faster than the speed of light. However, to those who see this new bridge (new topology), they will realize that you didn't actually travel faster than the speed of light, you just crossed a bridge. Construction of such bridges require exotic matter (i.e. negative mass energy).
Note that according to any realistic energy conditions in the universe (such as the averaged null energy condition), topological censorship conjecture holds. This conjecture states that we cannot actively probe any bridges in space-time; i.e. all topologies are causally disconnected from us outside the topology, so you cannot fly from earth through a wormhole, and then come back to earth. One can passively probe these topologies either by observing them from the past (i.e. seeing light from a white hole), or by entering a wormhole in such a way that one cannot return back (being "causally disconnected").
A: The speed of light can be slower than c.
wikipedia: Propagation_of_light_in_non-inertial_reference_frames
So there can be things going faster in one frame than the slow light of another frame.
