Gravity is in the Earth's Crust not the Core
Most have difficulty visualizing how the mechanics of a hollow earth operate. Throw into the mix the idea of a hole at each pole and people really start to get confused. The best way to clear up the confusion is to realize that the earth is a hollow shell much like those eggs you poke holes in at each end and blow the yolk out of. The real clincher, however, is that gravity is centered in the Earth's crust not at its core! ... So, instead of being a point-source, the center of gravity is actually spread out at the center of the crust.
The image above helps to illustrate this point. As someone sails around the lip of the opening at the pole, you are never aware that you have just entered the inner earth opening other than a brazen solar "mirage" which is actually the inner sun. As you sail around the lip, gravity is constantly pulling towards the center of the crust so that you never notice a change in gravitational attraction. Perhaps this is why early explorers who did not have GPS made maps with a continent at the northern extremities as they did not realize that they had actually made their way to the inside of the Earth!
Advocates of mainstream science use Gaussian mathematics to argue that in a hollow earth model, all gravitational forces cancel each other out. If the Earth is indeed hollow, then gravity is a slightly more complicated (or simple) phenomenon than can be explained with Gaussian physics and the current scientific theory of gravity is in need of an overhaul.