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I have to nitpick here,
Every system has an ultimate thermodynamic fate as a
black hole, even if the only way to get there is via QM tunneling.
Case I: no QM allowed; but GR is allowed (i.e. black holes are allowed)
If the Universe consisted of the "spherical" Sun and the "spherical uniform
density" earth only, orbiting at roughly the current earth-sun density. The
ultimate fate is the earth orbiting the sun and is not a black hole
Case II: QM allowed
Let's say we finally have reached the ultimate state of a black hole (I'm
not agreeing that this has to happen; I'm just examining that particular
case). Then Hawking radiation affect would occur and the BH would evaporate
away until we had some sort of bath of thermodynamically distributed
elementary particles (for the most part) through out the Universe.