A typical stellar-mass black hole of 3.3 solar masses has a radius of 10 km, 10,000 meters. At 100 meters outside the event horizon there is a 10:1 time dilation. At 1 meter outside there is a 100:1 time dilation. At 1 cm outside there is a 1000:1 time dilation.
But because you're traveling at almost the speed of light while you're falling in, it only takes you a few microseconds to fall past these points and get to the event horizon. If there was a mirror 1 mm outside the event horizon, a photon could start from 1000 km away, fall in, hit the mirror, and climb back out in 1/100th of a second, even allowing for time dilation. The spaceship will only spend a very tiny fraction of a second in the high time dilation area, even as seen from outside.
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Shouldn’t we at least see a visible Doppler shift at least.
A typical stellar-mass black hole of 3.3 solar masses has a radius of 10 km, 10,000 meters. At 100 meters outside the event horizon there is a 10:1 time dilation. At 1 meter outside there is a 100:1 time dilation. At 1 cm outside there is a 1000:1 time dilation.
But because you're traveling at almost the speed of light while you're falling in, it only takes you a few microseconds to fall past these points and get to the event horizon. If there was a mirror 1 mm outside the event horizon, a photon could start from 1000 km away, fall in, hit the mirror, and climb back out in 1/100th of a second, even allowing for time dilation. The spaceship will only spend a very tiny fraction of a second in the high time dilation area, even as seen from outside.