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That is correct. From the point of view of the infalling object, however, nothing changes as he crosses it except his position in space.

I say who gives a shit about the point of view of the infalling object. :-)

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It seems to me, intuitively, that the infalling object should experience inverse time dilation and extreme blue-shifting of the outside universe as it approaches the event horizon. Due to length contraction, that energy would be increasingly perpendicular to the object's trajectory, approaching a point where it is bombarded with enough energy to either knock it off its trajectory or "smear" its particles into orbit around the massive object (basically another sort of firewall).

Presumably the mathematical descriptions tell a different story because I never see it described like this.

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