You Could Be Inside a Black Hole Right Now – Adam Brown

[00:00:00]So suppose, um, one learns all these equations, but then finds himself in the unfortunate position of falling into a black hole.

[00:00:07]What would they see?

[00:00:08]>> Great question. So, there's actually two different perspectives you could take. One is the perspective for me watching you falling into the black hole.

[00:00:18]The other is the perspective of you falling into the black hole. And those two perspectives are consistent with each other, but interestingly different.

[00:00:25]So, maybe I should describe them both.

[00:00:27]So, first let's ask the question, what do I see as you fall into the black hole?

[00:00:31]What I see, this is of course how you how fast you need to how hard you need to fire your rocket to as not fall into the black hole, but you're not going to do this. You're just going to sit here a long, long way away from the black hole.

[00:00:41]You're going to turn off your rocket and accept what comes. And what comes is you'll slowly accelerate towards the black hole with a rate first given by the Newtonian formula, and then when you get close to the black black hole, start picking up corrections. Start picking up general relativity corrections to the Newtonian inverse square law.

[00:00:59]Um, and so what I will see as I watch you fall towards the black hole is first, you'll go faster and faster and faster towards the black hole as you fall down the gravitational potential of the black hole.

[00:01:10]Uh, and faster and faster and faster, but then something strange will happen, which is you'll stop going faster and you'll start going slower.

[00:01:16]And the reason you're going slower is that as I watch you, you start to get gravitational time dilation as you fall down here, and I see start to see you running slow, your clock running slow.

[00:01:28]This is the formula for if you were static. You're not static, you're moving. So, there's a some other formula, but the formula has the same effect, which is that as you get closer and closer towards the black hole, your wristwatch starts running slower and slower and slower.

[00:01:42]And in fact, if you do the appropriate integral, I never see you cross the event horizon. I just see you getting closer and closer to the event horizon, but slowing and slowing and slowing as you get closer and closer to the event horizon.

[00:01:53]Uh, and as I watch you, I'm presumably using light to watch you, that light gets more and more red-shifted. The wavelength gets longer and longer.

[00:02:02]Uh the longer the wavelength of light, the harder it is even to really see you.

[00:02:05]I start getting You start getting delocalized by the wavelength of the light.

[00:02:09]And eventually I just stop seeing you entirely. There's a final photon that I see that that you emit, and then you just fade to black, fade through red to black. I never see you cross the event horizon.

[00:02:21]Uh this was noticed by by people in the early days of of of general relativity and and greatly confused them. And they started to think that something you would experience something funny yourself as you fell across the event horizon. That is that is not true. In fact, if I instead adopt the perspective of you, from your point of view, your clock isn't running slow, it's running at 1 second per second. If you look back at me, there's some some funny stuff going on to do with me me running fast perhaps, but as far as you're concerned, everything's totally normal.

[00:02:50]You accelerate towards the black hole.

[00:02:52]You're getting faster and faster and faster as you approach the black hole.

[00:02:56]And you just sail across the event horizon totally as as normal.

[00:03:00]The event horizon is not a particularly violent place for you. You can calculate the tidal forces um as you cross the event horizon, or as you approach and then across the event horizon, and they're not particularly big. Uh or rather for large black holes, they're not particularly big. For a solar mass black hole, they they would be pretty big and would be pretty painful for you. You'd find that the your feet are being attracted to the black hole uh much more vigorously than your head is cuz it's cuz it's cuz they're closer, uh and you end up getting getting stretched. But if I take a big enough black hole, uh you wouldn't notice anything funny happening whatsoever.

[00:03:32]Um the the bigger the black hole, the smaller the the tidal effects. And if I took a black hole the mass of the galaxy, uh you'd be basically fine as you cross the event horizon. If I took an even bigger black hole than that, uh you could live out your entire life uh having crossed the event horizon of the black hole um before you hit the singularity, which is fatal. Um, when you cross the event horizon, uh, you are doomed.

[00:03:59]You are doomed because, uh, once you cross the event horizon, you must proceed to the singularity. There's no way you can fire a rocket to stop yourself uh, hitting the singularity. You are doomed, but you are not dead. Uh, you are only for sure dead once you hit the singularity and get spaghettified, get mangled by the by the tidal forces. But, for a large enough black hole, uh, you can be doomed and not even know it. Uh, the event horizon is is really a not locally measurable quantity. It is a teleological fact. It says that once you have crossed the event horizon, you must proceed to the singularity, but it can take a long time to get there for a large enough black hole. Uh, you could in principle, for a large enough black hole, uh, live out uh, your entire life if you had a a black hole that was, you know, many light centuries across.

[00:04:46]Uh, you could live out your life, you could have descendants, all of whom live in the in inside the black hole, and only once you really approach the singularity, do the tidal forces get strong and kill you.

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