On the nature of the infinite fall toward the EH

[PeterDonis]

Alice and everything else that makes up the black hole will fall further and further away.

True for Alice, false for everything else. See my previous post.

One notion is that Alice will stop when she reaches the singularity

It's not a "notion"; it's an inescapable consequence of classical GR.

but that singularity doesn't seem reachable. PeterDonis stated there was nothing for Alice to his - just the vacuum of space. If that's true, everyone just keeps falling and the tidal forces should never get extreme.

Incorrect; see my previous post.

 

[PAllen]

I was only talking about an existing black hole. I wasn't trying to address exactly what happens when one forms.

But you said "the entire mass of of the black hole is concentrated on or very near its event horizon". This is pure and simply false.

In the scenario created a week or two ago, Alice drops into the black hole first. Bob remains outside the black hole and sees Alice approach the event horizon.
For as long as Bob remains outside the black hole, he can never see Alice cross the event horizon.

Then Bob drops. In that scenario, Bob will never cross paths with Alice. Instead, Alice and everything else that makes up the black hole will fall further and further away. One notion is that Alice will stop when she reaches the singularity, but that singularity doesn't seem reachable. PeterDonis stated there was nothing for Alice to his - just the vacuum of space. If that's true, everyone just keeps falling and the tidal forces should never get extreme.

In that scenario, it is true that Bob will never cross paths with Alice. The rest of what you suggest is false. Bob sees Alice as of when Alice crossed the horizon at the moment Bob crossed the horizon. As Bob get close enough to the singularity to be seriously spaghettified, Bob will see Alice as of when she was spaghettified. Bob will see every stage of Alice's unfortunate fate, as Bob suffers the same.

 

[PAllen]

If they are both freely falling in, this is correct; someone who free-falls in later can never catch up to someone who free-falls in earlier. (Things get more complicated if one or both of them can fire rockets to accelerate inward or outward, but I don't think we need to go into that here.)

Yes, this is true in terms of time of starting free fall (assuming the events are causally connected). However, free faller (Alice) starting from a static position very near the horizon being caught up to inside the horizon by someone free falling from much further away (Bob) timed to cross the horizon just after Alice crossed, is possible. Of course Bob started falling earlier, but crossed the horizon later.

 

[PeterDonis]

Yes, this is true in terms of time of starting free fall (assuming the events are causally connected). However, free faller (Alice) starting from a static position very near the horizon being caught up to inside the horizon by someone free falling from much further away (Bob) timed to cross the horizon just after Alice crossed, is possible. Of course Bob started falling earlier, but crossed the horizon later.

Yes, you're right, I should have been clearer that I was talking about two free-fallers starting from the same altitude.

 

[.Scott]

My assumption was that both Alice and Bob dropped from the same altitude. Also, I imagine that giving Alice a 24-hour head start should be more than enough to keep them separated forever.

When I suggested that Alice might hit something, I got this response:

A black hole spacetime is vacuum; there's nothing to hit. But I don't see what this has to do with space curvature.

When something reaches the singularity is either stops or otherwise accelerates or it doesn't. If it doesn't, then it will continue to increase its distance from everything that falls in behind it.
It seems as though the singularity is a self-fulfilling creation. If you assume there is something there to crash into, then that abrupt deceleration allows objects that follow to catch up and feel the extreme tidal forces. Otherwise, everything flows freely with only moderate tidal forces.

 

[PeterDonis]

When something reaches the singularity is either stops or otherwise accelerates or it doesn't.

No, the correct answer is "none of the above". The singularity is an "edge" of spacetime; there is no spacetime beyond it, so any worldline that reaches the singularity ceases to exist once it reaches it.

If you assume there is something there to crash into

There isn't. The singularity is not a place in space, it's an instant of time. Can you crash into next Tuesday?

Just to clarify, all this is according to classical GR. The standard view among physicists seems to be that quantum gravity effects will take over before the singularity is reached, so there won't actually be an "edge" to spacetime where worldlines just stop and objects cease to exist. However, whatever takes the place of that will be something that probably can't be modeled using a classical spacetime at all; it certainly won't be anything normal like decelerating to a stop.

 

[WannabeNewton]

When something reaches the singularity is either stops or otherwise accelerates or it doesn't.

Do you actually know how a singularity is defined in classical GR? I would strongly suggest reading chapter 9 of Wald "General Relativity" for a basic introduction to the formalism of singularities in classical GR. You can't just hand-wave this stuff, there's a mountain of formalism that comes with the concept of a singularity.

 

[.Scott]

No, the correct answer is "none of the above". The singularity is an "edge" of spacetime; there is no spacetime beyond it, so any worldline that reaches the singularity ceases to exist once it reaches it.

Does it totally cease to exist or does its charge and mass get added into the singularity? If the mass gets added in, does that mass now appear to be a stationary mass? Also, is the singularity a point or a sphere? I don't think that once a black hole has been established, the radius of this "singularity" can ever reach zero.

 

[.Scott]

Do you actually know how a singularity is defined in classical GR? I would strongly suggest reading chapter 9 of Wald "General Relativity" for a basic introduction to the formalism of singularities in classical GR. You can't just hand-wave this stuff, there's a mountain of formalism that comes with the concept of a singularity.

I'm hoping there's some way of showing that the tidal forces would inevitably reach the most extreme conditions without attacking a "mountain of formalism".

 

[PeterDonis]

Does it totally cease to exist or does its charge and mass get added into the singularity?

Yes. The infalling object ceases to exist at the singularity, but its mass and charge are added to the mass and charge of the hole. Strictly speaking, the mass and charge of the hole are not "at" the singularity, because the singularity is not a place in space. The mass and charge are really properties of the spacetime as a whole. As far as an observer outside the hole's horizon is concerned, the mass and charge of the infalling object are added to the hole's mass and charge, at the latest, when the object crosses the horizon. (I say "at the latest" because the details depend on where the object falls in, relative to where the observer outside the horizon is.)

If the mass gets added in, does that mass now appear to be a stationary mass?

This question isn't really well-defined as it stands. See above.

Also, is the singularity a point or a sphere?

Neither. It's an instant of time.

I don't think that once a black hole has been established, the radius of this "singularity" can ever reach zero.

The singularity doesn't "reach" a radius of zero; it *is* at a "radius" of zero--but "radius" isn't really the right term, because, once again, the singularity, $r = 0$, is not a place in space; it's an instant of time.

As far as how the singularity forms, it forms when the object that originally collapses to form the hole reaches zero size and infinite density. Up to that point, $r = 0$ is a (non-singular) place in space, at the center of the object (we're talking about an idealized, perfectly spherically symmetrical collapse here, to keep things simple; non-symmetrical collapses just make the math more complicated, so that it requires numerical simulations, without changing the key conclusions); but at the instant the collapsing object reaches zero size and infinite density, the singularity forms and $r = 0$ becomes an instant of time.

 

[.Scott]

Strictly speaking, the mass and charge of the hole are not "at" the singularity, because the singularity is not a place in space. The mass and charge are really properties of the spacetime as a whole. As far as an observer outside the hole's horizon is concerned, the mass and charge of the infalling object are added to the hole's mass and charge, at the latest, when the object crosses the horizon. (I say "at the latest" because the details depend on where the object falls in, relative to where the observer outside the horizon is.)

The singularity doesn't "reach" a radius of zero; it *is* at a "radius" of zero--but "radius" isn't really the right term, because, once again, the singularity, $r = 0$, is not a place in space; it's an instant of time.

As far as how the singularity forms, it forms when the object that originally collapses to form the hole reaches zero size and infinite density. Up to that point, $r = 0$ is a (non-singular) place in space, at the center of the object (we're talking about an idealized, perfectly spherically symmetrical collapse here, to keep things simple; non-symmetrical collapses just make the math more complicated, so that it requires numerical simulations, without changing the key conclusions); but at the instant the collapsing object reaches zero size and infinite density, the singularity forms and $r = 0$ becomes an instant of time.

So when material is said to fall into the singularity, it's not a movement through space but though time? ...To reach that "instant of time".

But is it possible to reach this singularity without also reaching an r=0 position? I suspect the answer is yes.

 

[.Scott]

This just in: Stephen Hawking has completely remodeled black holes, eliminating the event horizon and spaghettification and replacing it with a "wall of fire".

 

[Mike Holland]

HJi guys, I've been following this revival of this topic, and I have one query. Once Alice passes the EV, all light she emits will be directed inwards, towards the singularity. So how can Bob ever catch up with this light after he crosses the EH, and see her getting spaggettified?
Surely there is no light moving towards him after he enters the BH. except from behind him.
Mike

 

[.Scott]

HJi guys, I've been following this revival of this topic, and I have one query. Once Alice passes the EV, all light she emits will be directed inwards, towards the singularity. So how can Bob ever catch up with this light after he crosses the EH, and see her getting spaggettified?
Surely there is no light moving towards him after he enters the BH. except from behind him.
Mike

If Alice is pointing her flashlight outward, Bob can catch up to some of this light after he falls through the event horizon.

 

[WannabeNewton]

HJi guys, I've been following this revival of this topic, and I have one query. Once Alice passes the EV, all light she emits will be directed inwards, towards the singularity. So how can Bob ever catch up with this light after he crosses the EH, and see her getting spaggettified?

Your question is easily answered by means of a simple Kruskal diagram. In fact your question is almost identical to one of the homework problems I had in a GR class last semester. Unfortunately I can't pull up the solutions publicly from my own university website for the class but I did find the exact same problem set assigned by some other university-they use an Eddington-Finkelstein diagram but the idea is the same: http://dafix.uark.edu/~danielk/Relativity/HW8Soln.pdf

See section 11.1.5 of the following document for the general formalism of Kruskal diagrams: http://eagle.phys.utk.edu/guidry/astro490/lectures/lecture490_ch11.pdf

 

[PeterDonis]

So when material is said to fall into the singularity, it's not a movement through space but though time?

Correct. Whether or not the object moves through "space" as well depends on what coordinates you adopt; most common coordinate charts have the infalling object moving through space as well as it falls. The key point is that the reason the singularity is unavoidable once

But is it possible to reach this singularity without also reaching an r=0 position? I suspect the answer is yes.

You suspect incorrectly. The answer is "mu": the question itself is not well-defined, because r = 0 is not a "position"; it's an instant of time. It's true that there are many possible spatial positions that you could be in when you reach this instant of time, just as there are many possible spatial positions you could be in when you reach next Tuesday at precisely noon GMT. But *all* of the spatial positions you could be in when you reach the singularity are labeled with r = 0, just as all of the spatial positions you could be in when you reach next Tuesday at precisely noon GMT are labeled as "noon GMT". The label "r = 0" labels an instant of time, not a place in space.

 

[PeterDonis]

If Alice is pointing her flashlight outward, Bob can catch up to some of this light after he falls through the event horizon.

Correct. But when he catches up to it, he (and it) will be at a *smaller* value of $r$ then Alice was when she emitted the light. So the light does fall inward towards the singularity; it just falls slower than Alice does, so Bob can catch up to it.

 

[.Scott]

Correct. Whether or not the object moves through "space" as well depends on what coordinates you adopt; most common coordinate charts have the infalling object moving through space as well as it falls. The key point is that the reason the singularity is unavoidable once

If the object is traveling through time to reach the singularity, should it take a shorter or longer period of time to reach it depending on when the object starts it journey?

You suspect incorrectly. The answer is "mu": the question itself is not well-defined, because r = 0 is not a "position"; it's an instant of time. It's true that there are many possible spatial positions that you could be in when you reach this instant of time, just as there are many possible spatial positions you could be in when you reach next Tuesday at precisely noon GMT. But *all* of the spatial positions you could be in when you reach the singularity are labeled with r = 0, just as all of the spatial positions you could be in when you reach next Tuesday at precisely noon GMT are labeled as "noon GMT". The label "r = 0" labels an instant of time, not a place in space.

Excellent. Then why is extreme spaghettification presumed?

 

[PeterDonis]

If the object is traveling through time to reach the singularity

It's only traveling through time in the same sense that everything "travels through time"; the infaller's "travel through time" to the singularity is no different from your "travel through time" to tomorrow.

should it take a shorter or longer period of time to reach it depending on when the object starts it journey?

Not depending on when it starts, no. The time to fall depends on how far above the hole's horizon the object starts.

Then why is extreme spaghettification presumed?

It's not presumed, it's derived by solving the Einstein Field Equation. The solution that applies to a black hole shows that tidal gravity increases without bound as the singularity is approached.

 

[PAllen]

This just in: Stephen Hawking has completely remodeled black holes, eliminating the event horizon and spaghettification and replacing it with a "wall of fire".

He just replaced a true horizon with an apparent horizon, which makes virtually no difference to discussions on this thread. His paper rejects the firewall hypothesis. It would help to actually read the paper.

 

[.Scott]

He just replaced a true horizon with an apparent horizon, which makes virtually no difference to discussions on this thread. His paper rejects the firewall hypothesis. It would help to actually read the paper.

When I first posted, I couldn't find a link to the original paper. But now, here it is:
http://arxiv.org/pdf/1401.5761v1.pdf
I'm not sure whether it makes a difference or not. He's saying that below this apparent horizon is a chaotic layer with the ability to so scramble energy that, in effect, information is lost. That doesn't sound like a healthy place to be.

 

[PAllen]

When I first posted, I couldn't find a link to the original paper. But now, here it is:
http://arxiv.org/pdf/1401.5761v1.pdf
I'm not sure whether it makes a difference or not. He's saying that below this apparent horizon is a chaotic layer with the ability to so scramble energy that, in effect, information is lost. That doesn't sound like a healthy place to be.

It may not be healthy, but it is just a result of noting that the classical no hair theorems say nothing about interior of apparent horizon (they describe exterior observations), and real collapses can't have perfect symmetries, so the interior will chaotically contain information about the details. Note, he claims information is not lost, only effectively inaccessible in the same sense as a chaotic classical system. My point is that macroscopically, his new picture is indistinguishable from a classical BH externally. Fall through the horizon is macroscopically the same as well. The difference is that the idea of an extended smooth interior fall until close to the singularity for an old, isolated, supermassive BH is no longer expected.