We often say, an observer near the horizon of a BH finds the light travelling from far outside the horizon blue shifted, or an observer away from the BH finds the red shift of light from near the horizon. We get a conclusion that a clock near the horizon goes faster than a clocker far outside the horizon.

But can red shift alone determine the time rate? As we know, in special relatity, when two men move toward each other, one finds blue shift of light from the other, but he also finds the clock of the other observer slower, not faster.

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