No, it's near the mantle.
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Well, of course, if it weren't fictitious, you would be right. In the movie, they say that it is near the core, which is impossible, due to the mantle, but also because of the gravity. And since the guy on the Nebuchadnezzar probably meant that it was near the Mantel, even then the gravity would make that impossible, or, extremely uncomfortable, right?
If there's no gravity in the centre of a sphere, then why would there be pressure from the rock above you? OR does that have nothing to do with gravity? But if it does, then that rock above you shouldn't matter, shouldn't it?
It's because the Earth is rigid. Imagine pushing a pencil into dough. The only force is at the top of the pencil. But because the pencil can't be compressed, that pushes the bottom of the pencil, down into the dough, even though the force isn't being caused there. It's the same at the centre of the Earth. Think of the column of dirt above your head. There's no gravity pushing the dirt at the bottom of the column down, but further up the column is being pushed down by gravity.