I must confess I don’t understand why, and I do think I’ve run far enough away to safely wonder why it’s a subjective eternity of pain - the observer falling into a singularity should see themselves falling in normally, and it’s only a faraway observer that could never see them enter, right?
If you were falling directly into the hole, that would be true, but that’s not how singularity power extraction works.
Your additional mass (and not splitting apart at the opportune moment) is going to screw up the orbit, but you’re gonna be frame-dragged through the ergosphere, looping around and around and around but not quite crossing the event horizon, for a very, very long time. Lots of opportunities to slow-mo-contemplate your poor life choices.
You falling into a singularity would result in the moment of your death lasting until eternity (sounds horrific, but means that at any point prior to the heat death of the universe, it might be possible to mount a rescue mission to you)
The actual term of art is “spaghettification,” where your body is stretched out into something most closely resembling a spaghetti noodle.
Wait, the sign says the ‘subjective’ timespan of your agony. Shouldn’t it say ‘objective’ timespan? Insofar as you can have a objective reference frame.
By the reference frame of whoever fell in, their death will last mere miliseconds. I suppose it wouldn’t make for quite as poignant a warning sign if it said that your death will be very quick and painless…
As mentioned above, black hole power generation doesn’t involve firing masses directly into the hole. You aren’t a proper power-generation slug, but being injected on its skimming course will put you on an exquisitely slow and painful orbit to oblivion.
Ah I see, I should’ve read more carefully. My bad.
Edit: Though, on further contemplation, I’d expect sphaghettification to kill you within the first pass, far from the ergosphere. Some searching suggests it would become lethal at as much as 10x the distance to the event horizon for a solar-mass black hole, and the ratio only increases at lower masses. I suppose maybe the angular momentum is very very high and so the ergosphere is spectacularly wide… no, I think things might start getting Weird™ if you had that much angular momentum.
Edit2: Although now that I think about it, if the black hole is instead very small, then even if the relative size of the event horizon and lethal radius is very high, the absolute size of the lethal radius could be fairly small. So then it comes down to your trajectory, because you’re basically skimming a small imaginary sphere that shears off whatever it touches. You could lose everything below the ankle, or everything below the neck due to a difference of a meter.
On further contemplation, I would firmly agree that your subjective agony would be over pretty quick, even if that agony is extended quite long from someone in flatter space-time; you see yourself as accelerating and moving around the mass based on velocities and accelerations measured in your frame of reference.
I’ll have to go look some things up later to be sure, but I suspect that the length of the agony in flat space-time would be fairly short, too. Because while the poor fool who tripped may be subject to time dilation, they’re also subject to some tens-hundreds-thousands of g.
I suspect there might only be something on the order of flattime minutes between “somewhat slow-motion person falling in” and “very slow motion gravitationally-sheared slurry falling in for all eternity”.