The other part of Einstein's general theory of relativity has been proven by NASA. It is true that gravitational forces (g forces) bend space and time (the space time continuum), like the curve of a tight cloth with a heavy object on it. Here is an idea on how to utilise this to flow through space and time, potentially for long distances or maybe even "times" (you would have to take the effects on time into consideration, if not to actually utilise it).
If you could get a object with a gravitational force, you could use it's effects on space and time to mobilise 'where' it goes, by directing it in relation to other forces towards the desired destination. Where do you find large enough gravitational forces? I think dark matter, which is vastly more available then carbon, is the most likely candidate. Dark matter has a gravitational force, and I guess the more you harvest, the more g forces you would have at your disposal. The greater percentage of the universe is dark matter. Get some near you today!
You would have to take larger g forces into consideration, using it's space time 'flow' to maneuver around it, like a judo expert. The way to map a path from point a to point b when there are other objects involved could be like considering the currents when using an underpowered boating vessel. When Christopher Columbus or Captain Cook or whoever it was was watching the waves on the shore which convinced him there was another continent, he was using the right observational skills for the task of mapping a path through the g forces of space and time at large. It isn't a matter (excuse the pun) of forcing a path, so much as using what is already happening.
A nice other effect of getting something along the lines of harvesting dark matter for it's g forces so as to bend space and time, is how little energy has to be expended in "fuel" to mobilise the effect of moving through space and time via gravity. There is no pollution, you simply use the g forces you have in relation to the g forces around you, like steering a sailing ship or using currents as a scuba diver. I think it is well worth researching this idea, as it could open horizons and decimate transport energy costs, especially in the long term/ long time/ long distance department. The financial and physical expenditure would be in setting it up, not using it. If you could bend the space time continuum enough, you could 'save' time especially when it relates to distance (space).
Actually, for something that takes up very little space and has a very dense gravitational pull is the matter in a white dwarf (a star that has gone through supernova, become a red giant, collapsed in on itself (imploded) and become the incredibly dense matter of a white dwarf. It has an intense gravitational pull, so you would only need a little of it (teaspoon). However, harvesting it could be tricky, considering it isn't nearly as available as dark matter, and it's incredible gravity would probably crush you before you even got close to it.
I have a little dream. This is pie in the sky, but I can see a metal electronic door, with a keyboard next to it. You walk up to the control panel, plug in the address of where you want to be, and then you step through the door and arrive at the destination, easily and instantly. But you have to bend the space time continuum at will to do that.