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You can't "scootch the material from the event horizon" because in the coordinates of anything approaching the hole, the matter does in fact fall in. However, you could study for example radiation from the matter. This is thought not to resolve the paradox for several reasons (note I gave a very similar answer to Can the event horizon save conservation laws ...


Unfocussing is convolving the image with a low-pass filter (that's what the optical system does to the source signal here). If high-frequencies are distroyed, you can't expect to recover them by simple algebra, since it would mean dividing by zero in the spectral domain. (filter high freqs are zero in real world, because the gaussian or the Bessel tails ...

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