> I think the coolest fact that I didn't grok until undergrad is that gravity relates to the stress-energy tensor and is not just due to rest mass alone. Which means that anything that has energy associated with it (i.e., everything we've ever observed) affects the gravitational field.

And not just energy, but tension. And tension is a signed quantity!

Imagine that you go out into deep (flat) space and build a large disk out of unobtanium, an extremely strong and rigid material. The ratio of the circumference to the disk to the radius is exactly pi. Now imagine trying to bring the disk to Earth's surface. Here space is curved by gravity, so the radius of a disk is just a bit longer relative to its circumference. So the disk has to flex! If it is rigid enough, it will want to spring back into flat space to minimize energy. You could imagine adding some gearing that would let you control this (anti-)gravity effect at will.

Calculating the material strength needed to make this effect usefully strong is left as an exercise to the reader.

(Disclaimer: this makes sense to me, but I am not a licensed antigravity engineer)