Thought experiment...if you built a bedroom sized room at the center of the Earth, and you are in that room, which way is down? For us, on the surface of the Earth, we can work out how strong gravity is. All you need is the mass of the Earth, the mass of a human, and the distance between the center of the Earth and the surface of the Earth. With no gravitational force, and no 'down', your room in the core of the Earth would have a space-time curve that was very flat. If there’s no net gravitational force, there can be no slant or directionality to space-time.

Source: Forbes January 31, 2017 20:37 UTC