So I'm pretty sure the artificial gravity system used in the movie Wall-e (on both the Axiom starship and on EVA) used a variable mass core to achieve flight, but the applications are different in both instances.
EVA's gravity field works against other objects in a limited range to power some sort of reactionless drive; it directs the force of gravity against another object and pushes off that object. She goes from motionless to breaking the sound barrier almost instantly, early on, and goes that same speed in space when able to act against the Axiom; it also makes sense that EVA would need a transport vessel with combustion-based rockets to break free of a planet's gravity and to travel back to the Axiom; once she's far enough from Earth, there's nothing for her own directed gravitational field to act against.
EVA's method of flight is not implied to be magnetic or static-based; there is no visible energy discharge, and her drive works in space FAR from the Axiom.
The Axiom has a much larger gravity field that seems to be acting on an earth-like scale; this again implies both a supermassive and supercompact object, as well as some method of energy maniuplation to amplify / contain the effects of the gravity. I imagine a giant black stone in a "reactor", with insane quantities of energy (probably Zero Point Energy, free energy, the science dismissing energy of the universe) being funneled into some sort of containment rig; the Axiom uses traditional rocket boosters, just like EVA's transport, but can go to a very fast speed without killing everyone aboard by increasing their mass to biologically lethal limits. It's not neccessary to assume the speed of light is achieved, because there isn't an actual distance from earth given to compare the travel time against; but it is STRONGLY hinted at that they travel faster than the speed of light, temporarily, seeing that the ship is "parked" next to a strange nebula.
Without requiring some sort of wormhole tunneling effect taking place, it's possible that the Axiom temporarily lowers it's mass to almost nothing, fires its boosters to maintain a linear heading, and then fires its "gravity drive" against some stationary object in the universe; some moon orbiting a planet, some sun, something that can resist the massive force sent slamming against it for a short period of time. It might knock these celestial objects out of alignment; it would fit with the politics of the movie if every time the ship exceeded lightspeed, it had to "litter" by knocking some moon or planetoid or star off course with a directed column of gravity.
If you do assume there's a wormhole at work, then the mass of the ship is still lessened by the gravity maintainment field to facilitate a faster travel time.
Even people who know what they're talking about aren't really sure how gravity works, so I don't feel like a total fucking jackass for writing this down. It's really pretty, really soft sci-fi.