Gravity on and inside a planet-sized bi-lobed body Admittedly, for yet another science-fiction project
Say I have a planet-like body shaped like a sphere with a torus subtracted out of it, leaving a sort of "apple core" shape.
Firstly, is the structure gravitationally stable, or would it collapse in on itself?
Mainly, I'm trying to assess the dynamics of gravity on the body, as there might be cultures on the outer (top and bottom) surfaces, on the torus-subtracted surfaces (the eaten flesh of the apple), and inside the lobes of the body, living in tunnels and caves bored into the crust.
To me, it seems that there are three basic ways this could go:

In scenario A, the gravity is still roughly similar to a spherical planet, with the two lobes interfering with each other to create a balance point in the center. In scenario B, the acceleration is focused towards the two lobes, but there's more of a "dead zone" where the gravity of the two lobes cancels each other out. Scenario B seems to act slightly more like a two-body problem. In Scenario C, the lobes are even more dominant, and they exert little stress overall on the central spindle. I figure this is more likely if the thing is rotating about its center, but NOT from top to bottom, so that the poles are sticking out from the eaten sides of the apple.
Questions relating to how the gravity of such a body would function: Would all the liquids (oceans, atmosphere) slip right into the torus rift, or would some of them stick to the top and bottom? Is the gravitational situation related to the size of the object (in that with a smaller object, the lobes would be close enough to influence each other more gravitationally)?
I apologize for my rudimentary physics knowledge.
 A: Unfortunately the answer to "is the structure gravitationally stable?" is "most definitely not." Anything planet-sized pretty much has to be close to a sphere, unless it's spinning very rapidly, because the gravitational forces increase with the body's size, whereas the electromagnetic forces holding atoms together don't, so the material's strength will always get overwhelmed.
If the body is spinning really fast there are several stable shapes it can take, including a two-lobed one that's very roughly a smoothed-out version of your shape, spinning end-over-end. In that case you can walk from any point to any other, and bodies of water could exist at any point on the surface. This is because the shape is defined by hydrostatic equilibrium - the surface settles down to a configuration where no part is much "higher" than any other in terms of gravitational potential. (The Earth bulges out at the equator because for this reason - it's spinning, but it's not spinning anywhere near fast enough to make it become a two-lobed structure.)
Your shape definitely isn't in hydrostatic equilibrium. Let's assume that it exists and isn't rapidly spinning, and that it's held together by magical tractor beams or something so it doesn't collapse into a sphere. Then because it's not in hydrostatic equilibrium, parts of it must in effect be huge mountains that stick far up out of the atmosphere. This means that both air and water would be found only in certain places - I would guess these would be in the centres of the top and bottom surfaces, and either in one ring or two separate rings around the central core. Everywhere else would just be vacuum, so getting from one habitable area to another would involve an unimaginably huge climb while wearing a space suit.
