There is no “space-time”; there is only “matter time.” Time is a product of the creation by photons; of matter. Matter is the evidence that time; or a change has occurred; without matter there is no record of change. Matter assembly is change recorded. The photon is the particle of time, causing gravitation; and the collection of matter. Forward motion; marked by spin revolutions; as increments of change in distance traveled; we label it as frequency. If matter didn’t exist there would be no time; no humans; no word called time.
Time travel can only be achieved by the single axis particle we call the photon. No-thing; else; can achieve that speed. Any other thing has too many directions of axial spin; and it disintegrates before it can reach light speed. The state of an atom in gyroscopic stability; does not lend itself to the speed of light travel. Having multiple axial spins is limiting to high speed for progression of motion. In fact, every atomic element has its particular statement of its own particular gyroscopic state of stability. Changing that code of stability changes the element.
Space is an empty no-thingness; by definition; avoid, where no change could exist or be noted; and by consequence; not even time could exist. Any effort to link space in time is an effort only designed to confound any truth in the separateness of either subject.