Anyway earlier this morning I had the strangest thought come into my head and it was, what would happen if the force of gravity that keeps us all, and everything else, more or less fixed to the surface of the Earth were to suddenly do a complete 180 and reverse itself. Could there actually some force of nature (like maybe the Core spinning in reverse or something) that could cause gravity to actually reverse in one sudden move so like if you're in a location where there's a ceiling above you or you're outside, would you find yourself falling like a rock, so to speak, and smashed into the opposing surface, or, if your outside, heading for certain doom while approaching the Earth's atmosphere.
Gravity is not caused by the spin of the Earth's core, nor is it caused by "pressure on the fabric of space," which I think is an overly literal misreading of a common analogy for how gravity operates. Gravity is a force of attraction between masses. Any two particles with mass exert a weak gravitational attraction on one another. It's a very tiny effect, which is why you don't feel yourself pulled toward your desk or your refrigerator. But a very large concentration of mass, such as a planet, exerts a strong enough attraction to pull and hold other things against it. If anything, the rotation of the Earth slightly counteracts its gravitational pull by creating a centrifugal effect, though that's minuscule. (It is enough, though, to give the Earth a slight equatorial bulge as it spins.)
There is no known physical mechanism that could turn the attractive force between masses into a repulsive force. However, it is currently believed that the universe contains a "dark energy" that acts as a very faint repulsive force, and that it will grow stronger over trillions of years to come, until it reaches the point that it overwhelms gravity and causes galaxies and stars to fly apart and prevents new solid bodies from forming. But that wouldn't actually reverse gravity itself, just cancel it out with an opposing force (the same way that the thrust of a rocket cancels out gravity and exerts enough additional force to let a spaceship escape the Earth).
More simply, if a sufficiently huge mass were to be placed directly over you, it might be enough to cancel out the pull of the Earth's gravity beneath you. Since the Earth's mass acts as if it's all concentrated at the Earth's center, 6,377 km below you, then if the mass were, say, 6.4 meters above you, then by the inverse square law it would only have to have one millionth of one millionth of the Earth's mass, though that would still be enormous. The late Dr. Robert Forward wrote about this in some of his nonfiction, conjecturing ways that a large amount of matter could be compressed into a degenerate state (like white dwarf matter) and used for this kind of "antigravity" effect. Of course, it would have to be held up by an incredibly strong set of supports. I sure as hell wouldn't want to stand under it. Heck, the Earth's crust probably couldn't support it; it would sink straight through.
As for what would happen in the imaginary circumstance of the Earth's gravity reversing itself, well, naturally anything not securely fastened would fall out into space. The atmosphere and hydrosphere (water) would escape into space, leaving the planet barren and uninhabitable. Soil, sand, and the like would fall away too. How many structures remained would depend on how solidly they were built and secured to the ground; many would probably stay in place at first but gradually break and fall away because they were engineered with compression rather than tension in mind.
The planet itself would remain largely intact, I think, because the electromagnetic forces that bind it are immensely stronger than gravitational forces. However, considering that the crust of the Earth is a set of overlapping plates floating on a bed of liquid magma, I suppose it's possible that if those plates suddenly found themselves on the "underside" (gravitationally speaking) of that liquid, they might simply fall away into space, breaking apart into chunks. The magma would also spill out into space, leaving the solid core. That would expand somewhat because it wouldn't be under gravitational compression anymore.
And if that core continued to exert an antigravitational field, I imagine it would accelerate out of Solar orbit and wander off into the galaxy, eventually being repelled away from the galaxy and into intergalactic space.