Hypothetically, if someone built an antigravity generator out of an exotic material that warped spacetime in an opposite way, so that matter was repelled instead of attracted, would the passage of time speed up for that frame of reference? I'm not a physicist or physics student, though I am a sci-fi writer interested in being as realistic as possible. It occurs to me that if negative energy densities and exotic matter do exist and have inverse gravitational properties, then inverse time dilation must also be a possibility. Given an antigravity generator of sufficient power, one could achieve impressive effects, ex. speeding up the passage of time in a certain region of space so much that for every second that passes outside the region, many years pass on the inside. Of course, the strong antigravity would make it very difficult for anyone to remain in this region of space for long, but I think I've already figured out a way around this problem. Given a spherical net of antigravity generators connected by filaments made out of another fantastic and nigh-unbreakable form of matter, the region of space at the center of the sphere should experience accelerated time without any harmful effects. The generators would be positioned so that they would cancel each other out, i.e. each object in the region is subjected to very strong antigravity, but from all sides equally. My first instinct was to assume that the objects in the center would be crushed into neutronium, but then I realized that this could only happen due to tidal gravity. If the central region is proportionally small enough (as compared to the entire volume of the sphere) that the strength of antigravity is roughly the same from every direction at every point in the region, then objects or people located in that region of space would feel no gravity at all... yet they would experience the reverse time dilation, because that would not be canceled out. Comments and objections are very much welcome. I consider myself reasonably well read in relativity and physics, but I wouldn't mind hearing from someone who really knows what they're talking about. Given the existence of these antigravity generators and a cable with incredible tensile strength to keep them from flying apart, would this device really work?