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Do tell how you generate energy from water at the bottom of a gravity well.

Tidal Power? Though the ocean is not strictly at the bottom of the gravity well. And I assume that's not really what you're asking.

That's from an external system, and won't work in the bottom of a hole.

There is no way, short of fusion that I know of. And fusion is not a valid answer in this context anyway (even if we had the tech for it).