How long would it take for a mini-black hole to eat the Earth?

How long would it take a primordial black hole to eat the earth if one fell to the center of it? Would it just sit there forever eating an atom at a time? (assuming event horizon the size of an atomic nucleus with 1,000,000,000 tonnes mass.)

A billion tons may seem like a lot, but it's actually miniscule compared to the mass of the Earth, which weighs about 6,000,000,000,000,000,000,000 tons! A black hole that weighs a billion tons would have an event horizon that's only about 10^-15 meters. So it would be so small that it would really only eat particles that happened to run into it, which wouldn't happen very often. If you were to plant it in the center of the Earth, it would just sit there forever, never consuming enough matter for anyone to notice.

If instead of setting it in the Earth's core, you were to drop it from the surface of the Earth, it would sink down through the middle, pop out the other side, and slide back and forth through the Earth for all eternity. If you assume that the black hole would only consume atoms that it happens to run into, then I calculate that it would take about 10^28 years for it to consume the entire Earth. This assumes that the black hole wouldn't lose any mass due to Hawking radiation. If you factor that in, it would probably *never* consume the whole Earth.

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