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Assuming that the black hole starts grow in the exact center of the planet and that the general structure of the planet does not degrade as it is eaten from the inside, would the gravity on the surface of the planet be affected by the black hole growing.

My uneducated guess is that as the matter becomes more compacted the gravity on the surface would actually decrease due to the fact that the distance to the mass, with respect to the surface, is increasing.

Also would the evaporation of the black hole actually decrease the total amount of mass in the center of the planet?

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Assuming that the center of the planet just collapses to a black hole, people on the surface won't notice any difference in gravity at all until the ground starts to fall out from under them (the planet will no longer be stable, as there will be no way to support the ground under your feet, ultimately).

This is due to a result known as Birchoff's theorem that says that one can treat any spherically symmetric mass distribution as if all of its mass were concentrated at it's center.

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Ah I see now, for every piece of matter that is now farther away from any given point on the surface there is an equal amount of matter that is closer as well. Would the total amount of matter actually decrease due to hawking radiation? – placeybordeaux Mar 28 '14 at 17:43
@PeterMichealLacey-Bordeaux: If you're taking about an Earth-sized black hole, you'd have to wait an age of the universe to see anything measurable, but probably. – Jerry Schirmer Mar 28 '14 at 19:11

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