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Approaching a black hole event horizon, I would see time pass more quickly outside.

In practical terms, let's assume I am approaching a supermassive black hole whose tidal forces I might survive at the horizon (let's say it's Saggitarius A*). I know that I wouldn't see infinite time pass as I crossed the horizon , but could I survive all the radiation from the "not quite infinite" amount of time (and presumably blue-shifted light?) I would be observing?

I've tagged this as "black-hole-firewall" because it sounds like a similar concept, but my question isn't motivated by information loss so I think it might be unrelated.

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    $\begingroup$ @safesphere what do you mean by "future light"? Can you highlight what part of the question needs clarifying? $\endgroup$ – quant Jan 27 at 3:57
  • $\begingroup$ @safesphere I don't think light "slows down and stops at the horizon". The accepted answer seems to address my question by the way, perhaps it will help to clarify things for your as well. $\endgroup$ – quant Jan 28 at 5:47
  • $\begingroup$ @safesphere I think what you're saying is that light from the even horizon for an observer at infinity ($t(r)$ in your example) would be infinitely redshifted (this is the mathematical singularity in the equation you linked). I don't see what this has to do with my question. In keeping with the notation of the paper you linked, I think you're looking at t when you should be looking at Tau. $\endgroup$ – quant Jan 28 at 7:04
  • $\begingroup$ @safesphere on a side note it took me quite a while to understand what you were saying because I found some of your wording a bit confusing. For example, when you say "the speed of light at the event horizon is zero" based on my limited understanding I don't think that's a meaningful statement in the context of GR. I ended up assuming you meant "the red shift of light emitted at the event horizon from the perspective of a distant observer is infinite". $\endgroup$ – quant Jan 28 at 7:05
  • $\begingroup$ @safesphere I think it's fair to say my previous comments already address this. $\endgroup$ – quant Jan 28 at 19:39
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It depends on exactly how you approach the horizon.

You mention the firewall but this is a quantum effect and is not universally accepted, so let's stick to classical general relativity. If you hover at a fixed distance outside the black hole event horizon then the light reaching you from the rest of universe is blue shifted and increased in intensity. As you reduce the distance from the horizon at which you hover then the blue shift and intensity increase and indeed go to infinity as you approach the horizon. In this case you can indeed add roasting to the ways a black hole can kill you.

However this only applies when you are hovering. If you are falling freely into the black hole then the light reaching you from the rest of the universe is red shifted not blue shifted. A rigorous proof of this is rather involved, but I give a heuristic proof in my answer to Do free falling observers see gravitational blueshift? You would fall through the horizon with any incendiary side effects.

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