General relativity says mass warps space. Special Relativity says that mass originates from energy:
........E
M = -----
.......C^2
The title of Einstein's 1905 paper was (in English):
Does the Inertia of a Body Depend on Its Energy Content? (one of two on special relativity that year)
So the above algebraic restatement of Einstein's iconic E = MC^2 recapitulates the question posed in the paper's title. (A tip of the hat to Frank Wilczek, for that.)
So, how are you going to warp space sufficiently without either a huge amount of mass, or a huge concentration of energy?
I know... Dilithium crystals and anti-matter, eh?
Sorry, the former is fiction; the latter takes orders of magnitude of energy more to generate it than is released in using it as fuel -- the most efficient in the universe, as far as anybody knows.
And how are you going to generate enough concentrated energy to warp space sufficiently without destroying yourself? Plus, your equivalent mass is related to that energy as well. Matter/anti-matter anialation is only so efficient. Plus, you still have to carry enough anti-matter and matter with which to anialate.
Sorry, people. No warp drives.
on edit: sorry about the equation. Ignore the dots.