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In special relativity when an object moves close to the speed of light it will appear redshifted due to time dilation. In addition the object will also appear to be length contracted.

But what about an object that will experience a gravitational time dilation, e.g. an object falling into a black hole? It will appear redshifted for a outside observer. But will it's length also appear to be contracted? If so wouldn't that mean, that an object falling into a black hole would basically appear to become flat (two-dimensional) at the Schwarzschild horizon (for an outside observer at infinity)?

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to an outside observer, the object falling into the black hole is progressively foreshortened into a pancake, any light coming from it becomes redder and dimmer, and the hands on a clock attached to it appear to go slower and slower as it gets closer and closer to the event horizon.

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