I've been told:

“As measured by proper time, a radially falling traveler quickly reaches and crosses the critical radius of a black hole. The reality that the traveler quickly reaches the critical radius appears to the distant observer to take an infinite amount of time because of the propagation of light.”

But let’s test this with a thought experiment:

Put a reflector on the back of the traveler as he freefalls towards the event horizon of a black hole. Have a distant observer periodically shine a light beam at the traveler. Use the Schwarzschild metric to calculate the radial location at which the faster moving light beam will overtake the slower moving traveler and reflect back to indicate the location of the traveler to the distant observer. No matter how much of a head start the traveler has before the light is turned on, according to the Schwarzschild metric the light will always overtake the traveler before the event horizon is reached. Let the distant observer continue to shine light beams at the traveler until the distant observer observes that the black hole evaporates because of Hawking radiation. Granted, this will take a long time. But the entire time, the reflected light will continue to reflect back from the traveler showing that the traveler fails to reach the event horizon before the black hole evaporates.

How can this be?

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