Is crossing a black hole's event horizon possible?

[physicurious]

As I understand things if you're hanging out in your space suit some distance away from a black holes event horizon and your buddy decides to dive on in you will never see him cross the event horizon. You'll see him approach the event horizon but never cross it. It would seem the time needed to cross the event horizon would be infinite. But we know black holes themselves eventually evaporate. It seems like from the perspective of your buddy on his black hole dive time would accelerate faster and faster until the black hole evaporated and never actually cross the event horizon. Does he cross the event horizon? What do we know about what actually might happen here?

 

[Ibix]

He crosses the event horizon and strikes the singularity in a finite and very short time, without seeing much of interest outside - certainly not time going faster. "Time stops at the event horizon" is a popular but wrong notion. What actually happens is that the natural coordinates used by a distant observer (basically based on radar timings) go badly wrong at the event horizon because no radar echoes can escape. But that doesn't mean you can't cross the event horizon. Concluding you can't is like concluding you can't walk through the north pole because it's the edge of the map.

Black hole evaporation is expected to cause black holes to evaporate in the very very far future. It won't save your friend.

 

[physicurious]

Ok. But from my perspective is there theoretically any point where I can say that he's crossed the event horizon? Forget some radar. Let's just say he's falling in with a flashlight pointed at me. Won't I just see that light become more and more red shifted but never disappear? Because from my perspective he never crosses? Or is there a point where he would cross and absolutely no photons from his flashlight would ever reach me?

 

[Ibix]

But from my perspective is there theoretically any point where I can say that he's crossed the event horizon?

Sure. Far from a black hole there are normally two changes in causal status. First when an event is no longer in your future lightcone it is no longer definitely in your future, and second when it enters your past lightcone it is definitely in your past. In between times whether it is in the future or the past is a matter of choice, but you can no longer do anything to affect it after it has left your future lightcone.

However, the event of a person crossing the event horizon leaves your future lightcone but never enters your past lightcone. From the moment it leaves your future lightcone you are powerless, even in principle, to stop it, whether you say it's in the future or the past. So you might as well say it's happened at that point, although different coordinate systems may or may not place it in the past.

Won't I just see that light become more and more red shifted but never disappear?

Yes.

Because from my perspective he never crosses?

That depends on your choice of perspective (more precisely, your choice of coordinate system).

Or is there a point where he would cross and absolutely no photons from his flashlight would ever reach me?

Classically, there is a last wave of light emitted before he crosses the horizon, but the redshift of it tends towards infinity and you would never receive all of it. Quantum mechanically there is a last photon emitted and you could receive it in finite time, but due to the statistical nature of QM you could never know it was actually the last photon and you would have to wait forever to confirm that there were no more.

 

[Orodruin]

This is a very common question. To make my usual analogy: An observer accelerating with constant proper acceleration in special relativity will have a so-called Rindler horizon. This means that there will be a large part of Minkowski space which is never in that observer’s causal past. Does that mean those events that are beyond that observer’s Rindler horizon never happen? Any inertial observer would certainly disagree.

 

[PeroK]

Ok. But from my perspective is there theoretically any point where I can say that he's crossed the event horizon? Forget some radar. Let's just say he's falling in with a flashlight pointed at me. Won't I just see that light become more and more red shifted but never disappear? Because from my perspective he never crosses? Or is there a point where he would cross and absolutely no photons from his flashlight would ever reach me?

It depends what you mean by "my perspective". If you formalise that, you end up saying "according to some specific system of coordinates". The question is then what is the physical significance of those specific coordinates? And what if those coordinates are themselves deficient in some way, in terms of describing certain events in spacetime?

 

[physicurious]

Rindler horizon, minkowski space, past/future light comes, chosen coordinate system. Can you all break this down for me so it's more comprehensible?

 

[Nugatory]

Ok. But from my perspective is there theoretically any point where I can say that he's crossed the event horizon? Forget some radar. Let's just say he's falling in with a flashlight pointed at me. Won't I just see that light become more and more red shifted but never disappear? Because from my perspective he never crosses? Or is there a point where he would cross and absolutely no photons from his flashlight would ever reach me?

Say that you are continuously broadcasting radio signals to your infalling friend. When they receive these signals they reply with a “received” signal. There is a point in time, not at all long after they start their fall, when you send a signal that they will receive but you will not receive a reply because they were inside the horizon when your signal was received. And very shortly after that you will send a signal that is never received because your friend dies at the “central” singularity before the signal has caught up with them.

We could reasonably consider the first moment to be the time when the friend passes through the horizon and the second to be the time the they reach the singularity.

While all of this is going on you are still seeng the ever more delayed and redshifted replies to the signals, or the light from his flashlight, all emitted before they passed through the horizon.

 

[Nugatory]

Rindler horizon, minkowski face, past/future light comes, chosen coordinate system. Can you all break this down for me so it's more comprehensible?

Yes, but not here. Get hold of Taylor and Wheeler’s book “Spacetime Physics”. The first edition is free on the internet and is comprehensible (although demanding) at the B high school level. The hardest part will be retraining your intuition about how time works.

 

[physicurious]

Yes, but not here. Get hold of Taylor and Wheeler’s book “Spacetime Physics”. The first edition is free on the internet and is comprehensible (although demanding) at the B high school level. The hardest part will be retraining your intuition about how time works.

Thanks!! Appreciate you!

 

[Ibix]

Thanks!! Appreciate you!

I'd strongly recommend getting more than one book. I like Taylor and Wheeler, but others here recommend Morin's Soecial Relativity for the Enthusiastic Beginner. The first chapter of that is free online and you're supposed to pay for more (but only £10 or so, I think). Ben Crowell, a former mentor here, wrote a couple of free-to-download textbooks that you can get from www.lightandmatter.com. His Relativity for Poets is about as good as you can get without going into maths, and there's an SR text with maths too.

 

[Grinkle]

@Nugatory Regarding post #8 - I think it is not possible in principle to verify that something (some beacon) has indeed crossed the EH. One would have to assume the crossing happened based on the last signal received and the likelihood that a crossing could have been avoided based on that last signal.

Do I need to be corrected? I'm not trying to split hairs - I am wondering if I am mistaken.

 

[Nugatory]

@Nugatory Regarding post #8 - I think it is not possible in principle to verify that something (some beacon) has indeed crossed the EH. One would have to assume the crossing happened based on the last signal received and the likelihood that a crossing could have been avoided based on that last signal.

You are right, we cannot directly observe the crossing. We just calculate when it happens (for any of several sensible definitions of "when"). That's sufficient to respond to the frequent "never crosses the horizon" misunderstandings and the question in the original post of this thread.

(It's worth adding that there are many things that we do not directly observe. The misunderstanding around reaching the horizon has less to do with our inability to directly observe than with the confusion created by a perverse definition of "when" the horizon is reached.)

 

[PeterDonis]

One would have to assume the crossing happened based on the last signal received and the likelihood that a crossing could have been avoided based on that last signal.

We can do more than that. We can predict what we would have observed if the object had not crossed--for example, if it fired rockets to hold itself just above the horizon--and see that we don't observe those things. If the object fired rockets to hold itself just above the horizon, we would continue to receive signals from it; they wouldn't stop coming. So when we don't see that happen, we know the object didn't stop just above the horizon.

In principle one could concoct a scenario where the object stopped so close to the horizon that its signals are redshifted to the point where we can't detect them. However, doing that would require a huge amount of rocket power--to the point where the extra rocket fuel the object would have to carry to stop itself for any appreciable length of time would make it more massive than the black hole it was falling into. So this is not a practical possibility.

 

[Nugatory]

I think it is not possible in principle to verify that something (some beacon) has indeed crossed the EH.

There's an assumption in the discussion so far that the mass of the infalling object is negligible. If the black hole has mass $M$ and we drop an object with small but non-negligible mass $m$ into it, we will very quickly end up with a black hole of mass $M+m$, which could reasonably be considered the verification you're looking for.

 

[PeterDonis]

If the black hole has mass $M$ and we drop an object with small but non-negligible mass $m$ into it, we will very quickly end up with a black hole of mass $M+m$, which could reasonably be considered the verification you're looking for.

Actually, we will detect the mass increase as soon as the object of mass $m$ falls past us--i.e., before it crosses the horizon. So we can't use that to confirm that the object has crossed the horizon. In fact, to us, the mass will be $M + m$ even if the object doesn't cross the horizon--if, for example, it fires rockets to hover above the horizon.

 

[Nugatory]

Actually, we will detect the mass increase as soon as the object of mass m falls past us--i.e., before it crosses the horizon. So we can't use that to confirm that the object has crossed the horizon. In fact, to us, the mass will be M+m even if the object doesn't cross the horizon--if, for example, it fires rockets to hover above the horizon.

Even if it is hovering below “where” the horizon of a black hole of mass $M+m$ would be? I suppose so - the configuration is not spherically symmetrical so I can’t just appeal to Birkhoff’s theorem, it’s more complicated.

 

[PeterDonis]

Even if it is hovering below “where” the horizon of a black hole of mass $M+m$ would be?

If the mass $m$ doesn't fall through the horizon, the hole itself only has mass $M$; the mass of the spacetime overall is $M + m$, but not all of that mass is contained in the black hole portion.

I can’t just appeal to Birkhoff’s theorem

No, because the mass $m$ is not vacuum, and Birkhoff's theorem assumes a vacuum spacetime. (Spherical symmetry is also broken, yes.)

 

[Ibix]

Even if it is hovering below “where” the horizon of a black hole of mass $M+m$ would be? I suppose so - the configuration is not spherically symmetrical so I can’t just appeal to Birkhoff’s theorem, it’s more complicated.

I think it's easier to see if you drop a thin spherical shell of mass on to the hole. Then it's obvious you see the gravitational change as the shell passes you, but it could consist of a shell of small powerful rockets that could stop arbitrarily close to the horizon and return.

 

[pervect]

Rindler horizon, minkowski space, past/future light comes, chosen coordinate system. Can you all break this down for me so it's more comprehensible?

Consider a spaceship accelerating at a constant acceleration of (approximately) 1 earth gravity, about 10 m/s^2, also approximately 1 light year / year^2.

This sort of motion, the motion of an object with a constant "proper acceleration" is called "hyperbolic motion". While there are wikipedia articles on the topic, they are rather dense, and may not be understandable. Searching the references referred to in the Wiki article for further reading may or may not help. I will give the references anyway, https://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity), as they will at least indicate that I'm not just making all this stuff up. (Sadly, with the state of the internet, a large amount of caution is needed about what one reads. I can't exclude myself - while I try to be accurate, I make mistakes - I'm not as reliable as something one might read in a better source, such as a textbook. That's one reason why we try to give referernces to what we say on PF. It also helps us, as writers, to make less errors, even though we are not perfect. At least I am not.)

Let's talk about the physical facts. Hyperbolae have what's known as an asymptote, and the physical interpretation of this aymptote is that light signals, emitted from Earth 1 year after the spaceship launch, will never reach the spaceship.

To say this let formally, a spaceship CAN outrun a light beam, if it has enough of a head start, and the spaceship continues to accelerate. The space-ship never exceeds the speed of light, but because of it's head start, the light, even though it always moves faster than the spaceship, can never quite catch up to it. This may be surprising, but on a space-time diagram the light beam is just the "asymptote" of a "hyperbola", the "hyperbola" of the "hyperbolic motion". Wiki has an article on this, too, but it doesn't look very helpful to me, I'll leave it for the reader to look up if interested.

This, so far, is all from the Earth point of view. Now, let's talk about the spaceship point of view. The idea of a point of view is not unique in general relativity, but the common choice of "point of view" for this situation is called "Rindler coordinates". There's a wiki on this, too, but much like the previous wiki, it is too short to really grasp the details, though it provides references. See for instance https://en.wikipedia.org/wiki/Rindler_coordinates. But don't be too surprised if the references are also too advanced to fully understand. I can't say whether they will be or not, not knowing your background, but it's not unlikely that you would have to do significant study to get enough background to fully understand the references. My goal, however, is to try to explain what happens without the math. We'll see if I succeede, it's hard to be sufficiently precise yet also understandable without the math :(.

Now, what happens from the perspective of the spaceship that's outrunning the light beam? I.e. what happens in these "Rindler coordinates?". Well, signals emitted from the Earth as time go on get more and more redshifted. If one uses an interpretation of the equivalence principle in which acceleration of an elevator is thought of as "gravity", the Earth is in a pseudo "gravity-well", the light emitted from the space-ship has to climb "up" the well to reach the spaceship. And at a certain "depth" in this well, light just can't make the climb. This particular "depth" in the "well" is the Rindler horizon, and as Orodruin points out, it's quite analogous to a black hole horizon.

A space-time diagram may or may not be helpful to you. If it is helpful, wiki has one in their article about "Rindler coordinates" , at https://en.wikipedia.org/wiki/Rindler_coordinates#/media/File:Rindler_chart.svg. The space-time diagram is good because it shows the hyperbola and it's asymptotes that I was trying to describe in text. The diagram actually shows several hyperbolae, corresponding to spaceships with different accelerations.

In the spaceship analogy, it's clear that just because the spaceship never sees what happens after 1 year of Earth time, because no signal emitted at or after that can catch up to the spaceship (as long as it continues to accelerate), that the events on Earth "still happen". Not being able to receive a signal from something, and/or refusing to put a label on the time at which something happens, doesn't mean that it "never happened". Another classical example of refusing to put a label on the time something happens at, and using that to claiming that it "never happens" because of that is known as "Zeno's paradox", which might also be helpful in understanding what's going on.

 

[srb7677]

Hi, I am new to this forum but have an interest in cosmology, though I am going to be far less learned than most of you appear to be. But my mind has grappled with a paradox regarding black holes. Assuming that somehow an astronaut falling into the black hole could survive the experience which is unlikely, does not the gravity well of a black hole make time pass more slowly as he falls nearer relative to the outside world? Does this not mean that whilst the astronaut experiences time normally, rapidly crosses the event horizon to be quickly crushed out of existence, if he could observe the outside universe as he fell would not time in it get ever faster from his perspective as he fell? And would not an outside observer see time for the falling astronaut pass ever more slowly?

And would not the slowness of his descent become infinite from our perspective as he reached the event horizon, ie time would stop at that point and we would never see him fall in? And for him looking out would not the passage of time accelerate as he reached the horizon to an almost infinitely fast rate? So that the universe itself will have ended by the time he crosses? Time distortion taken to its maximum at the horizon would tend to suggest this. And yet the logical paradoxes are mind-boggling to behold. And clearly black holes have grown since their creation so it cannot possibly be the case that nothing crosses the event horizon until the end of time.

I cannot get my head around the maths, so I am trying to understand without recourse to it. But I guess such things are only explicable mathematically.

 

[Grinkle]

My B level perspective, fwiw -

I find it impossible, myself, to avoid thinking in terms of what some might call a preferred frame when considering GR / black hole scenarios. I also assume only men would be silly enough to dive into a black hole and watch each other do so. ;-) As the traveler approaches the singularity, his clock is running normally as far as he is concerned and he reaches the singularity quickly on his clock - nothing slows down for him, and this happens in a finite amount of the traveler's proper time. The outside observer can calculate how much of his own (observer frame) proper time he expects would have elapsed before the traveler reached the singularity, and assume that event has occurred, even though he observes something different - he is still observing the red-shifted signals the traveler emitted on the outside of the event horizon, and will continue to observe these for as long as he has instruments sensitive enough to detect the further and further red-shifted traveler signal.

When I say I can't help but adopt preferred frame thinking, what I mean is that in my mind, the calculation of the observer (in which the traveler has reached the singularity) is more real than the red-shifted signal observations of the observer which indicate the traveler has not crossed the EH.

 

[srb7677]

Indeed it would be silly for anyone to ever jump into a black hole just to see what happens. In terms of common sense it would be something akin to jumping into a giant meat grinder just to see what happens. Insofar as black holes are concerned two lethal facts immediately spring to mind. Firstly all the superheated matter also falling in and emitting lethal levels of radiation and heat. And secondly the fact that the intensity of it's gravity increases so sharply over such short distances, that an astronaut's feet would feel a much greater gravitational pull than his head, ripping him apart and stretching the atoms he consists of out in a process picturesquely dubbed "spaghettification".

 

[PeroK]

Hi, I am new to this forum but have an interest in cosmology, though I am going to be far less learned than most of you appear to be. But my mind has grappled with a paradox regarding black holes. Assuming that somehow an astronaut falling into the black hole could survive the experience which is unlikely, does not the gravity well of a black hole make time pass more slowly as he falls nearer relative to the outside world?

Not in any physically meaningful way.



Does this not mean that whilst the astronaut experiences time normally, rapidly crosses the event horizon to be quickly crushed out of existence, if he could observe the outside universe as he fell would not time in it get ever faster from his perspective as he fell?

No. This is not the case.

And would not an outside observer see time for the falling astronaut pass ever more slowly?

"Seeing time pass" is an unphysical description. Light from those events takes ever longer to reach a distant observer. And no light from the event horizon or beyond ever reaches the distant observer. But, light reaching you is not the determining factor of whether an events happens.

And would not the slowness of his descent become infinite from our perspective as he reached the event horizon, ie time would stop at that point and we would never see him fall in?

Not in any meaningful way.

And for him looking out would not the passage of time accelerate as he reached the horizon to an almost infinitely fast rate?

No.

So that the universe itself will have ended by the time he crosses?

No. There is a last light signal that he will receive before crossing the horizon and before being crushed.

Time distortion taken to its maximum at the horizon would tend to suggest this.

Time distortion is not an accurate description of GR.

I cannot get my head around the maths,

Which is precisely the problem! The physics is robust; the paradoxes arise from your imprecise, non-mathematical description.


so I am trying to understand without recourse to it. But I guess such things are only explicable mathematically.

Exactly.

There is a thread somewhere on here where I calculated the last light signals to reach an infalling observer.

The reply functionality no longer works properly on my humble cell phone. See my answers in line above.

 

[Orodruin]

I cannot get my head around the maths, so I am trying to understand without recourse to it. But I guess such things are only explicable mathematically.

Non-mathematical and popular descriptions are by their very nature inexact and basing any sort of argument on them is going to be shaky at best and directly misleading at worst. If you cannot grasp the maths/theory, then you are indeed ultimately going to be confined to at some point just accepting a “that’s not how the theory works”.

 

[PeterDonis]

does not the gravity well of a black hole make time pass more slowly as he falls nearer relative to the outside world?

The concept of "gravity well" doesn't really make sense at and inside the horizon. Also, there is no invariant way to compare "the rate of time passing" between spatially separated observers in curved spacetime. So this question is not well-defined.

if he could observe the outside universe as he fell would not time in it get ever faster from his perspective as he fell?

No. As the astronaut falls, he will see light coming to him from the rest of the universe becoming more and more redshifted, and he will therefore see things happening in the rest of the universe more and more slowly.

time would stop at that point

No. The astronaut's clock continues to run just fine as he crosses the horizon.

we would never see him fall in?

This is correct, but not for the reason you give. It isn't that "time stops" at the horizon. Rather, the outgoing light emitted by the astronaut as he falls takes longer and longer to get back out to the distant observer as the astronaut approaches the horizon; and at the horizon, the outgoing light emitted by the astronaut as he falls is stuck at the horizon forever; it never gets back out. That is why we never see it.

 

[Ibix]

Assuming that somehow an astronaut falling into the black hole could survive the experience which is unlikely,

It's actually easy for a large black hole, except for the radiation from the accretion disc. It's only small black holes where the tidal forces kill you outside the horizon.

does not the gravity well of a black hole make time pass more slowly as he falls nearer relative to the outside world?

Not really. In this case the "time passes more slowly" rule of thumb fails, because it's only really unambiguously true for hovering observers. There is a finite time an infalling observer can experience before they hit the singularity, and only a finite part of the history of the universe is visible in that time.

 

[Demystifier]

As I understand things if you're hanging out in your space suit some distance away from a black holes event horizon and your buddy decides to dive on in you will never see him cross the event horizon. You'll see him approach the event horizon but never cross it. It would seem the time needed to cross the event horizon would be infinite. But we know black holes themselves eventually evaporate. It seems like from the perspective of your buddy on his black hole dive time would accelerate faster and faster until the black hole evaporated and never actually cross the event horizon. Does he cross the event horizon? What do we know about what actually might happen here?

In classical GR you can cross the horizon, even if nobody outside can see it. But as soon as we take quantum effects into account, nobody really knows. The black hole evaporation is a quantum effect, and there is the black hole information paradox associated with it. Some proposals for the solution of the information paradox introduce the firewall at the horizon, which prevents you from crossing the horizon.

 

[martinbn]

In classical GR you can cross the horizon, even if nobody outside can see it. But as soon as we take quantum effects into account, nobody really knows. The black hole evaporation is a quantum effect, and there is the black hole information paradox associated with it. Some proposals for the solution of the information paradox introduce the firewall at the horizon, which prevents you from crossing the horizon.

off topic: Why would the quantum effects be non-negligible for all black holes? For example a very large spherical formation of many galaxies, where we are at the centre, could be collapsing toward us. Then the event horizon will form and grow out to meet the shell. We could be crossing it right now. Why should there be quantum effects preventing that?

 

[Demystifier]

off topic: Why would the quantum effects be non-negligible for all black holes? For example a very large spherical formation of many galaxies, where we are at the centre, could be collapsing toward us. Then the event horizon will form and grow out to meet the shell. We could be crossing it right now. Why should there be quantum effects preventing that?

There are many ways to answer the question, neither of course being completely satisfying because we do not have a full theory of quantum gravity.

One answer is because it avoids the information paradox.

Another answer is because general covariance may only be a symmetry of classical theory, not of the full quantum theory, so in dealing with quantum effects you are not allowed to change coordinates from Schwarzschild to Kruskal, so the Schwarzschild singularity becomes a true physical singularity, rather than just a coordinate singularity.

Yet another answer is that quantum effects can be significant even for large objects. Consider, for instance, heat capacity of a big object, it cannot be understood without quantum physics.

 

[martinbn]

There are many ways to answer the question, neither of course being completely satisfying because we do not have a full theory of quantum gravity.

One answer is because it avoids the information paradox.

Another answer is because general covariance may only be a symmetry of classical theory, not of the full quantum theory, so in dealing with quantum effects you are not allowed to change coordinates from Schwarzschild to Kruskal, so the Schwarzschild singularity becomes a true physical singularity, rather than just a coordinate singularity.

Yet another answer is that quantum effects can be significant even for large objects. Consider, for instance, heat capacity of a big object, it cannot be understood without quantum physics.

Yes, but my point is that all this should also happen in a regime where classical gravity is very accurate. If there is an effect in that regime we should have noticed it by now.

 

[Demystifier]

Yes, but my point is that all this should also happen in a regime where classical gravity is very accurate. If there is an effect in that regime we should have noticed it by now.

Can you give an example of such a regime?

 

[martinbn]

Can you give an example of such a regime?

I did.

For example a very large spherical formation of many galaxies, where we are at the centre, could be collapsing toward us. Then the event horizon will form and grow out to meet the shell. We could be crossing it right now.

 

[srb7677]

The concept of "gravity well" doesn't really make sense at and inside the horizon. Also, there is no invariant way to compare "the rate of time passing" between spatially separated observers in curved spacetime. So this question is not well-defined.


No. As the astronaut falls, he will see light coming to him from the rest of the universe becoming more and more redshifted, and he will therefore see things happening in the rest of the universe more and more slowly.


No. The astronaut's clock continues to run just fine as he crosses the horizon.


This is correct, but not for the reason you give. It isn't that "time stops" at the horizon. Rather, the outgoing light emitted by the astronaut as he falls takes longer and longer to get back out to the distant observer as the astronaut approaches the horizon; and at the horizon, the outgoing light emitted by the astronaut as he falls is stuck at the horizon forever; it never gets back out. That is why we never see it.

Thanks for your clarifications. It is a food job I am here to learn rather than preach. Most of you are far more knowledgeable in this area than I am.

 

[Tomas Vencl]

off topic: Why would the quantum effects be non-negligible for all black holes? For example a very large spherical formation of many galaxies, where we are at the centre, could be collapsing toward us. Then the event horizon will form and grow out to meet the shell. We could be crossing it right now. Why should there be quantum effects preventing that?

While I agree with Demystifier's remark and can imagine a situation where, for example, quantum evaporation generates a different metric (with a firewall), I think that in the given example of a 'galactic collapsing shell with Earth in the middle,' there really can be no observable effects of crossing the horizon. The formation of the horizon inside the shell is a global effect and depends on how the shell will behave in the future (for example, whether it will stop its collapse, which is theoretically possible beyond its horizon). If I were to observe any effect of crossing the horizon on Earth, I would retrocausally gain information about the future behavior of the shell, which would likely lead to some paradoxes.