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Conditions for Schwarzschild Metric to be applicable

The Wikipedia article regarding the two-body problem in General Relativity states that the Schwarzschild metric "corresponds to the external gravitational field of a stationary, uncharged, non-...
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Does matter stacks up as it approaches Black hole?

When something approaches Black hole it'll experience time dilation with respect to a frame away from the black hole. So to an observer away from the hole the object would seem to slow down until ...
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