Can You Fall Into a Black Hole? Exploring Time & Decay

[Matt204823545]

TL;DR Summary

Many things about a black hole seem contradictory

It takes infinite amount of time to cross the event horizon from an outsider's perspective. But black holes eventually decay from Hawking radiation. So if you wait long enough a black hole won't exist anymore, as it would have decayed into nothing.

The in-falling observer witnesses infinite years pass outside as they fall into the black hole. Therefore they should witness the decaying of every black hole in the universe, including the one they're falling into. So, eventually they should stop falling and find themselves in a cold, dark, empty universe, because the black hole will have ceased to exist long before they even reached the event horizon.

Or does their black hole still exist because it's downstream of space-time and so it hasn't had time to decay yet in the observer's perspective?

If the singularity were a ring and the observer could fly through it to the other side, would they then witness only a single black hole (the one they emerged from) in the universe, or will it decay away into nothing as they passed through the ring? Because it seems incorrect to have only 1 black hole in existence, but it also seems incorrect for it to decay because the observer didn't get near enough to the ring to witness it decaying. What really happens here?

 

[Ibix]

It takes infinite amount of time to cross the event horizon from an outsider's perspective.

For a classical black hole that doesn't evaporate, yes. Evaporating black holes behave differently - you will see the objects fall in as the hole evaporates.

The in-falling observer witnesses infinite years pass outside as they fall into the black hole.

No - there is a finite last time that you can see before you strike the singularity.

If the singularity were a ring

The singularity is a ring in Kerr black holes. Passing through it allows you to loop back round and meet yourself - although for various reasons we don't really believe that to be a realistic model of the interior of a black hole.

 

[Grinkle]

you will see the objects fall in as the hole evaporates.

I will try to ask this in an answerable manner. If my question makes no sense, apologies in advance.

If there were a physics lab at the BH at the center of the Milky Way, say it was 1 LY distant from the EH of that black hole, or if some other distance makes the question more sensible, whatever distance that is, and a beacon is fired at the event horizon at 0.5 c relative to the physics lab, how much time would the clock on the physics lab measure before the beacon was observed to cross the EH?

I don't care about the numbers above, its just my attempt to better frame the question. If changing them helps answer, please do. The basic question is "how long before I see something cross the EH?"

 

[phinds]

how much time would the clock on the physics lab measure before the beacon was observed to cross the EH?

Did you not understand post #2?

To reiterate:

Infinite, as stated in the thread already, unless the BH does in fact evaporate in which case only many orders of magnitude times the current age of the universe(*). AGAIN, as already stated in the thread.

Actually, in terms of the evaporation time of a good-sized BH, the current age of the universe isn't even a rounding error.

 

[Ibix]

If there were a physics lab at the BH at the center of the Milky Way, say it was 1 LY distant from the EH of that black hole, or if some other distance makes the question more sensible, whatever distance that is, and a beacon is fired at the event horizon at 0.5 c relative to the physics lab, how much time would the clock on the physics lab measure before the beacon was observed to cross the EH?

If you assume that the black hole is a purely classical black hole, like a Schwarzschild or Kerr black hole, then the answer is infinite time. The light from the event of the beason crossing is forever trapped at the horizon.

However, if the hole evaporates then light from the horizon escapes when the horizon no longer exists. That's a timescale of many billions of years (net evaporation can't start until the CMB is cooler than the black hole, which is a long way off), and the black hole evaporating is likely to make light from one particular event in its history difficult to spot, but it's there in principle.

 

[Nugatory]

The in-falling observer witnesses infinite years pass outside as they fall into the black hole.

You’ll hear this a lot, but it’s not true. The infaller does not witness the entire future history of the outside universe. They experience only a very short amount of time and see only what happens during that time before they reach the singularity and die.

Suppose that you are falling into a black hole while I am sending you a steady stream of radio messages, one every second. Whenever you receive on of these messages, you reply with your current position (there are some subtleties about how this is defined, but they don’t matter here). I send my message at time $T_1$ and at time $T_2$ I receive your reply saying that your current position is $X$; I conclude that that’s where you were at time $(T_2-T_1)/2$ because the radio signals had to make the round trip from me to you and back again.

As you approach the event horizon $T_2-T_1$, the time between transmission and reply, will increase without bound and no matter how long I wait I’ll never get a reply from you at the event horizon. That’s what it means to say that according to an outside observer it takes an infinite amount of time to reach the event horizon.

Your experience, however, is different. You receive a steady stream of messages from me as you fall through the event horizon and towards the central singularity. One of those messages will be the last thing you see before you die at the singularity, and it will have been sent only a very short time after you started your fall and long long before the black hole hypothetically might evaporate.

(All of this is assuming that the black hole is large enough that tidal forces are survivable throughout your fall - otherwise you’re like spaghettified and dead before you even reach the horizon)

 

[Matt204823545]

You’ll hear this a lot, but it’s not true. The infaller does not witness the entire future history of the outside universe. They experience only a very short amount of time and see only what happens during that time before they reach the singularity and die.

But that seems contradictory, I'll try to explain why.
1. We have the fact that an outsider observer will never witness the infalling observer cross the event horizon because time slows down to almost zero as they approach the event horizon, from the perspective of the outsider observer, hence it takes an infinite amount of years for the infalling observer to cross the event horizon.
2. Therefore the infalling observer should see the opposite occurring when they look back at the outside observer, they should see the outside observer's time speeding up and so infinite outside-years should pass as the infalling observer crosses the event horizon.
I don't see how one can refute those two things because they're direct opposites of each other.

 

[Ibix]

I don't see how one can refute those two things because they're direct opposites of each other.

It's easy - the outside observer bounces radar pulses of the infaller. He says the echo event happened half way between the time he emitted the pulse and the time he received it. If the infaller passes through the horizon then the outside observer never receives echos from radar pulses that catch the infaller after the crossing. That doesn't mean the pulses take infinite time to reach the infaller from the infaller's perspective.

The thing to realize is that the reciprocal relationship between tick rates only exists between hovering clocks. And a clock crossing the horizon is, by definition, not hovering.

 

[Grinkle]

Did you not understand post #2?

My snip came from this sentence -

Evaporating black holes behave differently - you will see the objects fall in as the hole evaporates.

I did not include enough to give the context.

And for the record, I am quite confident I did not understand post 2. ;-)

 

[phinds]

However, if the hole evaporates then light from the horizon escapes when the horizon no longer exists. That's a timescale of many billions of years (net evaporation can't start until the CMB is cooler than the black hole, which is a long way off), and the black hole evaporating is likely to make light from one particular event in its history difficult to spot, but it's there in principle.

Actually, I think "billions of years" wouldn't even be a rounding error on the time involved. Billions of years is roughly 10E9, but let's be wildly generous and say you meant trillions. That would be 10E12, and you said many, so make it 10E14. BH evaporation of a modest sized BH is estimated to be on the order to 10E60, so the amount you suggested (much MORE than that amount actually) is one part in 10E46. I really don't think that counts as even a rounding error unless you want to take things out to 46 decimal places.

Supermassive BHs take about 10E80.

 

[phinds]

And for the record, I am quite confident I did not understand post 2. ;-)

OK. If the rest of the thread hasn't cleared things up for you, what can we help you with, specifically. Still confused about evaporating BHs?

 

[PeroK]

But that seems contradictory, I'll try to explain why.
1. We have the fact that an outsider observer will never witness the infalling observer cross the event horizon because time slows down to almost zero as they approach the event horizon, from the perspective of the outsider observer, hence it takes an infinite amount of years for the infalling observer to cross the event horizon.
2. Therefore the infalling observer should see the opposite occurring when they look back at the outside observer, they should see the outside observer's time speeding up and so infinite outside-years should pass as the infalling observer crosses the event horizon.
I don't see how one can refute those two things because they're direct opposites of each other.

It's important to realize that something like "an outsider observer will never witness the infalling observer cross the event horizon because time slows down to almost zero as they approach the event horizon" is a popular science attempt to explain the science of black holes. That statement in this case does not stand up to scrutiny.

Any contradiction you have found is within the popular science rendering of the theory.

The theory of General Relativity - and black holes in particular - as presented in university textbooks, does not rely on logical deduction from popular science soundbites. Instead, it presents GR as a self-consistent theory of the geometry of spacetime. Within that theory, the infalling observer crosses the event horizon in finite time (by their clock) and does not "witness" the entire history of the universe.

 

[Nugatory]

We have the fact that an outsider observer will never witness the infalling observer cross the event horizon because time slows down to almost zero as they approach the event horizon, from the perspective of the outsider observer, hence it takes an infinite amount of years for the infalling observer to cross the event horizon.

“Time slows down” is another thing that you’ll hear a lot but that isn’t so. It’s a way of talking about what’s going on without requiring that your audience think too deeply (which is why you’ll hear it in popularizations but not real textbooks) and it will end up misleading you if you take it too seriously.

Look at post #6 above again: you are falling into the black hole and I conclude that you won't reach the event horizon even if I wait forever. That conclusion doesn't depend at all on "time slowing down" for you - I didn't even consider that. It comes from my (T2−T1)/2 calculation of the time that you sent a radio signal giving your current location; it's based on the time I measure for the signal to make the round trip from me to you and back again. Thus, it is not telling us anything about "time slowing down", it's telling us something about the paths through spacetime that the radio signals are taking.

Now let's think a bit more about what it might mean to say that "time is slowing down" (spoiler: taken literally, that phrase is somewhere between misleading and wrong):

Time passes for me at a rate of one second per second and if my wristwatch is working properly it will tick once per second. If I'm unsure about this I can test it in various ways. For example I might hold my hands 30 cm apart with a light source in one hand and a light detector and a very senstive stopwatch in the other. I turn on the the light source with one hand and start the stopwatch with the other; when the detector triggers I check the stopwatch and when it tells me that the light took one nanosecond to travel 30 cm I know that there's nothing strange about my seconds, they're exactly the right length. All of this works for me far outside the black hole and - crucially - it also works for you even if you're falling towards the black hole and through the event horizon. As far as you're concerned, time is passing at a rate of one second per second also.

If time is passing at the same rate of one second per second for both of us, what does "time is slowing down for you" mean? Well, suppose my wristwatch reads 12:00:00 and at the same time your wristwatch reads 12:00:00 (one or both of us can set our watches to make them agree). Then I wait ten seconds and look at my wristwatch again, and of course it reads 12:00:10. If at the same time that my watch reads 12:00:10 your watch reads something less, say 12:00:05, I'll say that your time is slow. But this doesn't have anything to do with the rate at which time is passing for either of us - it's a consequence of how we decided what was happening to you "at the same time" that I looked at my watch the second time.

But it turns out that there is no one universal standard for "at the same time". If this idea is at all new to you, you should google for "Einstein train simultaneity" to learn about the relativity of simultaneity - it is one of the key concepts that the popularizations generally skip over and without which relativity will be incomprehensible. Relativity of simultaneity is what's behind any comparison of clock readings and conclusions about time passing more or less quickly for different observers. It's how the velocity-based time dilation ("time slows down for fast-moving objects") works, and why when A and B are moving relative to one another we can correctly say that "A is at rest, B is moving, B's clock is slower than A's clock" and "A is moving, B is at rest, A's clock is slower than B's clock" without contradiction.

And in the original problem, where you're falling into the black hole and I'm outside it... the $(T_2-T_1)/2$ definition of "at the same time" from #6 makes sense for me, but it has the funny property that there is no "at the same time" for anything that happens to you at or below the event horizon.

 

[Grinkle]

Still confused about evaporating BHs?

Thanks - I think I understand now. When I read post 2, I wondered if the meaning was that when one takes into account quantum effects at the edge of the BH, observations at the macro level become markedly different even on human time scales. I now think the statement is that evaporation in principle allows one to, post-evaporation, potentially reconstruct the histories of objects that crossed what used to be the EH, pre-evaporation. But we are still talking about unimaginably long time scales.

 

[PeterDonis]

It takes infinite amount of time to cross the event horizon from an outsider's perspective. But black holes eventually decay from Hawking radiation. So if you wait long enough a black hole won't exist anymore, as it would have decayed into nothing.

No. See this Insights article:

https://www.physicsforums.com/insights/black-holes-really-exist/