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I believe if you gently step over the event horizon of a black hole, the light reflecting off the back of your head will wrap around accretion disk and back into your eyeballs. It requires a bit of setup and is kind of a one-time thing, but you'll get a much better view than you could get with a mirror!
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Small correction: You'll want to be at the photon sphere, not the event horizon (1.5x the Schwarzschild radius). You can theoretically hover there for an unlimited time, and even escape, as long as you don't mind the immense acceleration necessary. :)
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I tried this. On an unrelated note who's up for some spaghetti?
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This didn't work for me at first, but I tried it a second time and it actually worked! You weren't kidding about it being a one-time thing though, because I haven't been able to do it since.
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Next time you do it, remember what you did in your previous only attempts. It'll help make the only shot you have be successful for once, since once is all you get. If you keep at it, you'll get better with practice, and maybe eventually, you'll be able to make it happen for the first time.
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A friend of mine tried but it showed him with no-hair
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I see what you did there... I think... My head hurts...
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