What is the event horizon of a freefaller into a black hole?

[caveman1917]

Hawking radiation doesn't exist for freefallers. A free-falling observer sees nothing but the usual seethe of virtual pairs as he crosses the event horizon.

Grant Hutchison

Do you mean Hawking radiation only shows up for an observer at infinity, or only for non-inertial observers?

[grant hutchison]

Although this discussion is in terms of an abstract observer, I guess we don't really know if a real observer would be able to survive let alone observe; do we even know whether chemistry would still work with this swapping of time-like and space-like dimensions?

There's no effect locally: the swap of space and time is only according to the coordinates of a distant observer.

Similarly, if you could be dangled through the event horizon on a wire (bear with me!) then wouldn't the wire break at the event horizon because the forces holding the molecules together could be transmitted back to the cable outside?

The force required to support the wire would go to infinity as the tip of the wire approached the event horizon. So any wire will break at some point outside the event horizon.

Grant Hutchison

[grant hutchison]

Do you mean Hawking radiation only shows up for an observer at infinity, or only for non-inertial observers?

Non-inertial observers. Hawking radiation is analogous to the Unruh radiation observed by continuously accelerating observers, except in the case of Hawking one is accelerating in order to stay at a constant distance from the black hole.
If you lower a thermometer quasi-statically towards the event horizon, you'll see the temperature climb towards infinity at the event horizon, because the necessary acceleration to maintain a constant radial distance climbs towards infinity at the event horizon. Cut the rope, and that radiation bath disappears when the thermometer enters freefall.

Grant Hutchison

[Jeff Root]

The wire would definitely break. Any real wire would, of course,
break long before it could reach the event horizon. At the event
horizon the electromagnetic forces holding the atoms of the wire
together (and holding the electrons to the nuclei) are completely
unable to move upward at all. If you could magically hold an
atomic nucleus in place at the event horizon, its electrons would
be stripped away by the black hole's gravity, because the electric
force would not have any effect at all in countering the gravity.

All real materials would fail well outside the event horizon, which
is the point where even an ideal material would fail. Maybe it's
where Superman would be powdered.

On the other hand, a free-faller into a really big black hole would
not be affected at all. You and Tom could be eating lunch as you
fall through the event horizon of a supermassive black hole and
not notice that it happened. An hour or two later, though, you
would be turned into dinner as the tide spaghettifies you.

A free-faller always sees a shorter and shorter period of events
below him. Pretending that photons never run out and that your
eyes can see light nomatter how strongly redshifted, you would
see a long line of free-fallers preceeding you as you approach the
event horizon, but they would disappear one-by-one below you,
increasingly closer to the black hole's center, but also increasingly
closer to you. All along, you would see the free-fallers preceeding
you accelerating away from you. The farther ahead of you they
are, the greater the acceleration away from you. You would never
see anything ahead of you that you could not previously see.

-- Jeff, in Minneapolis

[tommac]

Let me try to reword my question:

-Lets isolate a system that includes just a BH and earth.
-Earth is in a freefall towards the black hole.
-The black hole is super super massive so that the event horizon for an external observer would be 1000 light years ( but there is no external observer in our system/universe ... just the BH and the earth )
-As we fall towards the BH our reference point gradually changes. In fact we will even be able to see light that is coming from inside the EH
-From our perspective as we approach the EH it appears to us to receed back towards teh singularity. ( THis is just from our perspective as a freefaller ) The EH is real but since we are in an isolated system and freefalling along with the gravitational flow we can see past the EH and continue to see stuff in front of us until basically it hits the singularity.
- The is a point in the space in front of us that we will never see any light .... from a distance it would be defined as the EH but as we approach the EH it would be somewhere inside the EH.
It seems from your post above that the above as stated is true ...

Now this is what I was trying to ask.

Lets say we had rockets on the earth that would allow us to escape as long as we ( earth ) didnt fall past the EH.
At the last minute we accelerate away from the BH at just below the speed of light ... at first hovering and only slightly moving ... then moving faster as the curvature of space time lessens.

There was some light ... inside the EH that we would have seen if we continued the freefall. So basically we would have crossed the EH and encountered the light ... but since we accelerated in the opposite direction we never encountered that light.

Is our movement relative to that photon superluminal?

There's the event horizon of the black hole, which is the same for everyone. That's easy to calculate, and is a global property of spacetime.
There's an event horizon for someone inside the black hole's event horizon, which is determined by the fact that there's a singularity in his future, and in the future of everything else inside the black hole. An infaller's view of his surroundings is therefore limited because photons from distant objects terminate in the singularity before the infaller sees them. The farther ahead of him an object is, the less of its sub-event-horizon history the infaller can (in principle) see. That event horizon is observer-dependent, and is also calculable, but it would be a complicated bit of maths. For a simple "eternal" black hole, it's drawn by the worldline of a photon emitted at the event horizon in the infinite past, and terminating at the singularity along with the worldline of the infaller. No event pastwards of that worldline can communicate with the infaller, because all photons from such events terminate in the singularity before the infaller gets there.


I have no idea what this means.

Grant Hutchison

[tommac]

BTW ... Jeff and Grant ... this really helps to clear things up for me ...

Is the free fallers event horizon called anything? Is there a way to refer to that?

[caveman1917]

Is the free fallers event horizon called anything? Is there a way to refer to that?

I'd say it's called an event horizon. If it's an invariant everyone calls it the same.

[Strange]

-As we fall towards the BH our reference point gradually changes. In fact we will even be able to see light that is coming from inside the EH

You will not be able to see light from anything inside the event horizon until you cross the event horizon.

-From our perspective as we approach the EH it appears to us to receed back towards teh singularity. ( THis is just from our perspective as a freefaller ) The EH is real but since we are in an isolated system and freefalling along with the gravitational flow we can see past the EH and continue to see stuff in front of us until basically it hits the singularity.
- The is a point in the space in front of us that we will never see any light .... from a distance it would be defined as the EH but as we approach the EH it would be somewhere inside the EH.

I don't think so; before you cross the event horizon you can only see light emitted outside the event horizon. After you cross the event horizon you can see light from objects some distane (time) ahead of you.

There was some light ... inside the EH that we would have seen if we continued the freefall. So basically we would have crossed the EH and encountered the light ... but since we accelerated in the opposite direction we never encountered that light.

You never see it because you never cross the event horizon.

Is our movement relative to that photon superluminal?

I'm not sure it makes any sense to compare your speed with something that you are completely isolated from. You are not accelerating "away" from the photon faster than light, it is being "bent" away from you by the curavture inside the event horizon.

[thothicabob]

Hmm. I think that if you've managed to get urself into a situation where this would even be of theoretical interest, you'd have a lot of other more pressing (or pulling) issues of a more practical nature to worry about...

[grant hutchison]

A free-faller always sees a shorter and shorter period of events
below him. Pretending that photons never run out and that your
eyes can see light nomatter how strongly redshifted, you would
see a long line of free-fallers preceeding you as you approach the
event horizon, but they would disappear one-by-one below you,
increasingly closer to the black hole's center, but also increasingly
closer to you.

I don't think this is the case, given that you have stipulated that we can always see photons if there's a light-like line connecting us to some distant event.
At whatever distance the freefaller is from the black hole, we can always find some photons just below the event horizon which will reach the singularity at the same moment as the freefaller. These mark the limit of what the freefaller can glimpse before reaching the singularity. In the freefaller's coordinates, these photons travel a large distance (about the same as the distance between the freefaller and the event horizon) before encountering the freefaller's eyes. So the freefaller sees a distant object when he encounters these photons. But he sees these objects extremely faintly and very redshifted, because a very short proportion of their history below the event horizon is smeared over the freefaller's entire history below the event horizon. What closes in around the observer is not an event horizon which prevents him seeing beyond a certain distance, but an event horizon which prevents him seeing beyond a certain time in the history of distant objects. That time differs for objects at different distances.

Grant Hutchison

[grant hutchison]

-As we fall towards the BH our reference point gradually changes. In fact we will even be able to see light that is coming from inside the EH

No, we won't. Not until we're inside the event horizon ourselves.

-From our perspective as we approach the EH it appears to us to receed back towards teh singularity. ( THis is just from our perspective as a freefaller )

No, it doesn't, for reasons I've explained above.

The EH is real but since we are in an isolated system and freefalling along with the gravitational flow we can see past the EH and continue to see stuff in front of us until basically it hits the singularity.

We can never see "past" the black hole's event horizon. We can only see things inside it when we are inside it.

- The is a point in the space in front of us that we will never see any light .... from a distance it would be defined as the EH but as we approach the EH it would be somewhere inside the EH.

No, as freefallers we can see light from arbitrarily large distances; we're just limited in how much future time we can see at each distance. The fact that small durations of distant time are smeared over larger durations of our own time makes distant objects faint and redshifted.

It seems from your post above that the above as stated is true ...

Then I have to guess that you've brought some huge preconception of your own to what I wrote.

Now this is what I was trying to ask.

See? You've once again blithely introduced something entirely new, and are telling us it is what you were "trying to ask" all along!

Lets say we had rockets on the earth that would allow us to escape as long as we ( earth ) didnt fall past the EH.
At the last minute we accelerate away from the BH at just below the speed of light ... at first hovering and only slightly moving ... then moving faster as the curvature of space time lessens.

There was some light ... inside the EH that we would have seen if we continued the freefall. So basically we would have crossed the EH and encountered the light ... but since we accelerated in the opposite direction we never encountered that light.

Is our movement relative to that photon superluminal?

The photon recedes from us faster than light, in your chosen coordinates. That's what happens in GR when you extend your local coordinates. Light only moves at c locally.

Grant Hutchison

[grant hutchison]

I'd say it's called an event horizon. If it's an invariant everyone calls it the same.

The black hole event horizon is an invariant; this event horizon we've been discussing, for infalling observers below the event horizon, isn't an invariant: every observer has his own, and in fact the observer can modify his own horizon a little by motoring around to shorten or lengthen the duration of his time below the black hole's event horizon and above the singularity.
But it's an event horizon nevertheless, since it partitions spacetime into events that can never be observed and events that can (in principle) be observed. It just has a temporal as well as a spacial component to it: we see more of the history of nearby objects than of distant objects. So it has similarities to the Rindler horizon of an accelerating observer, and the event horizon experienced by observers in a Universe that is undergoing accelerating expansion. I think such observer-dependent event horizons are called apparent, whereas the black hole's invariant event horizon is absolute.

Grant Hutchison

[galacsi]

We see the most direct evidence of this with gravitational lensing: http://en.wikipedia.org/wiki/Gravitational_lensing

Are you sure it is the same thing ? Gravitational lensing is a consequence of GR no ? The idea is rather intuitive , if mass distort space time , light can be bent. So a distant galaxy "A" can be seen as a circle or an arc, because of nearer galaxy "B" acting as a lense. But if I understand you , light emitted from the inside of a black hole radially will also be curved and could not escape the BH ?
Is there any schematics that you know showing it ?

[tommac]

You will not be able to see light from anything inside the event horizon until you cross the event horizon.

Yes but slightly irrelevant to the free faller since they are destined to cross the EH.

I'm not sure it makes any sense to compare your speed with something that you are completely isolated from. You are not accelerating "away" from the photon faster than light, it is being "bent" away from you by the curavture inside the event horizon.

I guess the spirit of the question was that it was something that unless you did something you would have encountered and only because you accelerated in the opposite direction did you escape from it. If it was initially "bent" away from you then how would you encounter it if you continued to free fall. I get your answer here but just trying to work out the symantics.

[tommac]

Wow ... where is the "like" button ;-)

I don't think this is the case, given that you have stipulated that we can always see photons if there's a light-like line connecting us to some distant event.
At whatever distance the freefaller is from the black hole, we can always find some photons just below the event horizon which will reach the singularity at the same moment as the freefaller. These mark the limit of what the freefaller can glimpse before reaching the singularity. In the freefaller's coordinates, these photons travel a large distance (about the same as the distance between the freefaller and the event horizon) before encountering the freefaller's eyes. So the freefaller sees a distant object when he encounters these photons. But he sees these objects extremely faintly and very redshifted, because a very short proportion of their history below the event horizon is smeared over the freefaller's entire history below the event horizon. What closes in around the observer is not an event horizon which prevents him seeing beyond a certain distance, but an event horizon which prevents him seeing beyond a certain time in the history of distant objects. That time differs for objects at different distances.

Grant Hutchison

[grant hutchison]

Are you sure it is the same thing ? Gravitational lensing is a consequence of GR no ? The idea is rather intuitive , if mass distort space time , light can be bent. So a distant galaxy "A" can be seen as a circle or an arc, because of nearer galaxy "B" acting as a lense. But if I understand you , light emitted from the inside of a black hole radially will also be curved and could not escape the BH ?

They are the same phenomena, as Strange says. The bending of spacetime within the event horizon is just so extreme that there is no "outward" direction for a photon to travel in. All directions lead to the singularity.

Grant Hutchison

[caveman1917]

The black hole event horizon is an invariant; this event horizon we've been discussing, for infalling observers below the event horizon, isn't an invariant: every observer has his own, and in fact the observer can modify his own horizon a little by motoring around to shorten or lengthen the duration of his time below the black hole's event horizon and above the singularity.
But it's an event horizon nevertheless, since it partitions spacetime into events that can never be observed and events that can (in principle) be observed. It just has a temporal as well as a spacial component to it: we see more of the history of nearby objects than of distant objects. So it has similarities to the Rindler horizon of an accelerating observer, and the event horizon experienced by observers in a Universe that is undergoing accelerating expansion. I think such observer-dependent event horizons are called apparent, whereas the black hole's invariant event horizon is absolute.

Grant Hutchison

Thanks, i thought the question was about the black hole event horizon as it pertains to infalling observers.

[tommac]

No, we won't. Not until we're inside the event horizon ourselves.

With respect ... will we see it or will we not see it? WE WILL. However, not until we're inside the event horizon ourselves. The difference in this wordind yours represents the point of that statement. We are freefalling , lets assume that we have no idea and no way to measure that we are crossing the EH AND that we have no way to change our current path. From our observation we will see continue to see light from the direction of the singularity. As an unknowing observer there is nothing that peculiar about what we are observing. If there is no external observer or no other reference to glean any additional information then wouldnt the EH be exactly what we are and will be able to observe if we do nothing? If we do nothing we can communicate in both directions with someone that is technically inside the EH. The fact that we will be inside the event horizon when we receive the message is on little consequence to the system in question ... correct?

I understand that the EH is real and that once we are inside we cant escape it ... but in this closed system what would escaping even mean?

[tommac]

No, as freefallers we can see light from arbitrarily large distances; we're just limited in how much future time we can see at each distance. The fact that small durations of distant time are smeared over larger durations of our own time makes distant objects faint and redshifted.

But wouldnt there be a place where the relative speed of photons relative to us and travelling towards us is actually moving away from us at the speed of light?

X0------X1------EH------X2-------X3--------X4-------X5--------X6-------S


Lets assume that X0 is a freefaller .... and his path is through points X1 EH ( event horizon ) X2,X3,X4,X5,X6 and then hits the singularity ... we see a flashlight falling in in front of us ... at X1 when we are at X0 etc ... when it is at X6 and we are at X5 couldnt the difference in velocities between us as freefallers and the flashlight as freefallers be greater than the c ? and if it is greater than c than wouldnt we not be able to see the light coming from that flashlight?

[tommac]

Thanks, i thought the question was about the black hole event horizon as it pertains to infalling observers.

Thanks Grant !!!! I missed this post somehow ... but that exactly answers my question here. And 100% clarifys everything.

[grant hutchison]

With respect ... will we see it or will we not see it? WE WILL. However, not until we're inside the event horizon ourselves.

So you need to stop saying ridiculous things like "we will even be able to see light that is coming from inside the EH" and "we can see past the EH". These statements are simply incorrect. "Coming from inside the EH" and "see past the EH" unequivocally imply light crossing the event horizon. Light doesn't cross event horizons.

The difference in this wordind yours represents the point of that statement. We are freefalling , lets assume that we have no idea and no way to measure that we are crossing the EH AND that we have no way to change our current path. From our observation we will see continue to see light from the direction of the singularity. As an unknowing observer there is nothing that peculiar about what we are observing. If there is no external observer or no other reference to glean any additional information then wouldnt the EH be exactly what we are and will be able to observe if we do nothing? If we do nothing we can communicate in both directions with someone that is technically inside the EH. The fact that we will be inside the event horizon when we receive the message is on little consequence to the system in question ... correct?

And if I drive with a paper bag over my head, and have a big shock absorber on the front of my car, and really good suspension, then I won't notice when I run over and kill a pedestrian. So that event is of little consequence to the system in question ... correct?

Grant Hutchison

[tommac]

Sorry ... one last follow up on this great post ... ( not a preconception ).

As a BHs EH is an invarient ... does the distance match for all metrics?

So lets say I am accelerating towards it
and another observer is accelerating away from it
and another observer is hovering around it
and another observer is in a deep gravitational well ...

Each with different set of metrics ... the EH can be measured by each of them as say 10km and they all would agree that it is 10 k? ( this is a question, I dont get how that can be ??? )

The black hole event horizon is an invariant; this event horizon we've been discussing, for infalling observers below the event horizon, isn't an invariant: every observer has his own, and in fact the observer can modify his own horizon a little by motoring around to shorten or lengthen the duration of his time below the black hole's event horizon and above the singularity.
But it's an event horizon nevertheless, since it partitions spacetime into events that can never be observed and events that can (in principle) be observed. It just has a temporal as well as a spacial component to it: we see more of the history of nearby objects than of distant objects. So it has similarities to the Rindler horizon of an accelerating observer, and the event horizon experienced by observers in a Universe that is undergoing accelerating expansion. I think such observer-dependent event horizons are called apparent, whereas the black hole's invariant event horizon is absolute.

Grant Hutchison

[grant hutchison]

But wouldnt there be a place where the relative speed of photons relative to us and travelling towards us is actually moving away from us at the speed of light?

X0------X1------EH------X2-------X3--------X4-------X5--------X6-------S


Lets assume that X0 is a freefaller .... and his path is through points X1 EH ( event horizon ) X2,X3,X4,X5,X6 and then hits the singularity ... we see a flashlight falling in in front of us ... at X1 when we are at X0 etc ... when it is at X6 and we are at X5 couldnt the difference in velocities between us as freefallers and the flashlight as freefallers be greater than the c ? and if it is greater than c than wouldnt we not be able to see the light coming from that flashlight?

But we'd be able to see the light from that flashlight earlier in its history. The light the flashlight emitted at EH stays at EH, and we see it as we pass EH. The light the flashlight emitted towards us at X2 falls towards the singularity more slowly than we do, and we may eventually catch up with it and see it as we pass (say) X5. So we can never see the light the flashlight emitted at X6, because it reaches the singularity before we do. But when we are at X5, we see the flashlight ahead of us, as it was at X2. We, the flashlight and its light are all well past X2 when we see that light, which brings us the image of a flashlight falling some distance ahead of us.

Grant Hutchison

[grant hutchison]

Sorry ... one last follow up on this great post ... ( not a preconception ).

As a BHs EH is an invarient ... does the distance match for all metrics?

So lets say I am accelerating towards it
and another observer is accelerating away from it
and another observer is hovering around it
and another observer is in a deep gravitational well ...

Each with different set of metrics ... the EH can be measured by each of them as say 10km and they all would agree that it is 10 k? ( this is a question, I dont get how that can be ??? )

It's invariant because it always marks a boundary between the same regions of spacetime. Observers always agree about which events are inside the black hole event horizon and which events are outside the black hole event horizon. (Hence the "event", hence the "horizon".) Distances are not invariant, so there's no reason the distance one observer measures should match the distance another observer measures.

Grant Hutchison

[grant hutchison]

Thanks, i thought the question was about the black hole event horizon as it pertains to infalling observers.

It's often difficult to know what's happening in one of tommac's threads.

Grant Hutchison

[tommac]

So you need to stop saying ridiculous things like "we will even be able to see light that is coming from inside the EH" and "we can see past the EH". These statements are simply incorrect. "Coming from inside the EH" and "see past the EH" unequivocally imply light crossing the event horizon. Light doesn't cross event horizons.

Are you saying that we cant see past the EH?
Are you saying that we cant see light that originated from inside the EH?

[tommac]

Thanks, i thought the question was about the black hole event horizon as it pertains to infalling observers.

Well it sort of does ... BUT grant cleared some things up in his answers.

From what I learned about this thread is that there is a difference between the invarient EH of the black hole ... and the apparent EH that is not invarient and particular to the observer. The freefaller can pass through the BH EH without noticing ... but the freefaller can never observe any event past his own variant EH.

I am still a little fuzzy about the consequences of each ... but learned quite a bit from the info that Grant provided.

Sorry for the confusion but it is a confusing topic ( especially from the freefallers viewpoint ).

[tommac]

Yes ... agreed. So at some point ... lets say X6 there is an apparent EH for the infaller (at x5 ) .

But we'd be able to see the light from that flashlight earlier in its history. The light the flashlight emitted at EH stays at EH, and we see it as we pass EH. The light the flashlight emitted towards us at X2 falls towards the singularity more slowly than we do, and we may eventually catch up with it and see it as we pass (say) X5. So we can never see the light the flashlight emitted at X6, because it reaches the singularity before we do. But when we are at X5, we see the flashlight ahead of us, as it was at X2. We, the flashlight and its light are all well past X2 when we see that light, which brings us the image of a flashlight falling some distance ahead of us.

Grant Hutchison

[tommac]

Ahhhhhhh .... so the distance is not invariant ... only the barrier .... interesting!!!
So what one observer could see as a 10km BH another could see as a 100000000km black hole.

Ummmm .... sorry one more follow up as I write this ...
Wouldnt that effect the density? wouldnt a 1 solar mass BH with a event horizon of 3km have a different density than a one solar mass black hole with a event horizon of 10km ( due to space-time curvature? )

It's invariant because it always marks a boundary between the same regions of spacetime. Observers always agree about which events are inside the black hole event horizon and which events are outside the black hole event horizon. (Hence the "event", hence the "horizon".) Distances are not invariant, so there's no reason the distance one observer measures should match the distance another observer measures.

Grant Hutchison

[Strange]

Are you saying that we cant see past the EH?
Are you saying that we cant see light that originated from inside the EH?

That is exactly what he is saying.