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Science question: Black Holes

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lets say that in march 2005 a baby black hole was created in a particle accelorator, and it was stable. How long would it take to reach the centre of the earth? And how long would it take to devour the whole earth?

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  1. It would never reach the center of the Earth, although it would eventually BECOME the center of the Earth.  Because the surface speed where the black hole was created would be non-zero, the black hole and the Earth would orbit their barycenter with a period of 24 hours.  Originating as a sub-atomic particle, it would behave as if it were a point mass in a vacuum.  Initial collisions with nuclei would result in large changes of momentum, but Newtonian celestial mechanics would continue to apply.  Accretion would be slowed by collision with electrons without collision with nuclei, giving the hole a comparatively massive negative charge which would tend to repel atoms.  That period of the hole's life would be relatively brief.

    When I originally contemplated this problem I forgot that the black hole would have an angular velocity, and concluded that it would devour the Earth in a matter of months or years.  Taking the angular velocity into account would seem to extend that time to millenia, or even a million years or so.

    Could this be the mechanism behind heretofore unexplained variations in "Chandler Wobble", or Plate Tectonics?

    The accretion would stop once the Earth was consumed, except for meteors, but with such a small collision cross-section accretion would be much slower than it is now.  The Moon would appear to have an "inexplicably" erratic orbit around the Sun.

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