Mass distribution of a black hole?

[cragar]

Why can't we know the mass distribution inside a black hole. If we are observing from outside the event horizon I couldn't tell how the mass was moving around inside the black hole, I could just figure out how much was in there by measuring the G field.

 

[Bill_K]

Because it's spherically symmetric. All you can tell is the total mass, not how it's distributed as a function of r. The same holds for Newtonian gravity: you can't tell from measuring the Earth's gravitational field how much mass is located in the mantle and how much in the core. From the outside it all looks the same.

 

[cragar]

suppose it wasn't uniformly distributed . I know what your saying its like a gauss's law argument

 

[Dale]

It doesn't matter if it is uniform or not, as long as it is spherically symmetric all you can determine is the total mass.

 

[cragar]

Ok suppose it wasn't spherically symmetric. Suppose I had a curtain around a circle and inside this circle I had a big heavy rock on one side and then 2 other lighter rocks randomly placed. classically I could tell the mass distribution by walking around the curtain and measuring the gravitational field . But in the case of a black hole where I have some big rocks entering a BH at random places, once they cross the event horizon I will not be able to map out the mass distribution by going around and measuring the G field.

 

[Dale]

But in the case of a black hole where I have some big rocks entering a BH at random places, once they cross the event horizon I will not be able to map out the mass distribution by going around and measuring the G field.

If it is not spherically symmetric then why not? Of course, with sufficiently strong gravity and enough time it will eventually become spherically symmetric, but until then you should be able to at least get some information about the distribution.

 

[cephron]

It doesn't matter if it is uniform or not, as long as it is spherically symmetric all you can determine is the total mass.

Suppose you're dealing with a BH with very high rotation. I may be out of date, but my understanding is that spinning BH => ring-shaped singularity?

In that case, mass distribution would have circular symmetry, but not spherical. Would one be able to determine the radius of the ring, perhaps?

 

[atyy]

It's usually said that black holes settle down quickly to a state where only three parameters observable from outside: mass, charge and angular momentum. The lingo seems to be that black holes have "no hair".

http://archive.ncsa.illinois.edu/Cyberia/NumRel/BlackHoleEvolution.html
http://jila.colorado.edu/~ajsh/insidebh/schw.html

Some proposed tests (which probably didn't get funded, but judging by the authors, the ideas are probably good): http://arxiv.org/abs/0903.0100

 

[Dale]

Suppose you're dealing with a BH with very high rotation. I may be out of date, but my understanding is that spinning BH => ring-shaped singularity?

In that case, mass distribution would have circular symmetry, but not spherical. Would one be able to determine the radius of the ring, perhaps?

Sure, my statements above would not apply to a rotating mass since the stress-energy tensor of a rotating mass is not spherically symmetric.

 

[cragar]

If it is not spherically symmetric then why not? Of course, with sufficiently strong gravity and enough time it will eventually become spherically symmetric, but until then you should be able to at least get some information about the distribution.

So then I could use this fact to communicate with people outside the BH . Let's say I went into the BH in a rocket, and let's say the black hole is pretty wide so that I am not ripped apart by tidal forces. When I cross the Event horizon . I could shoot off large heavy rockets and change the mass distribution and I could set up some kind of code with this. And have someone outside the BH hole measure the changes in the G field. So I could communicate with them what is going on inside the BH.

 

[Dale]

Hmm, interesting idea. I have no clear objection to it, but it does make me doubt the correctness of my previous statement.

 

[cephron]

Is it possible that the time dilation would screw it up? Again, I worry that I'm out of date (I read a teenager-level book on black holes a while back, which is where I remember most of my "knowledge" about BHs), but I was under the impression that time dilation inside a black hole was, for all intents and purposes, infinite?

 

[Q-reeus]

So then I could use this fact to communicate with people outside the BH . Let's say I went into the BH in a rocket, and let's say the black hole is pretty wide so that I am not ripped apart by tidal forces. When I cross the Event horizon . I could shoot off large heavy rockets and change the mass distribution and I could set up some kind of code with this. And have someone outside the BH hole measure the changes in the G field. So I could communicate with them what is going on inside the BH.

No way, at least according to the standard BH scenario. Relative to an observer outside the BH, time and even the speed of light asymptotically slows to zero for an infalling entity at the EH, and things wo'nt get any better further in (to the extent 'further in' has any meaning!). As far as the rest of the universe is concerned - you're in perfect deep freeze (as well as invisible and pancaked to zero thickness). Not much signalling going on here!

 

[cragar]

No way, at least according to the standard BH scenario. Relative to an observer outside the BH, time and even the speed of light asymptotically slows to zero for an infalling entity at the EH, and things wo'nt get any better further in (to the extent 'further in' has any meaning!). As far as the rest of the universe is concerned - you're in perfect deep freeze (as well as invisible and pancaked to zero thickness). Not much signalling going on here!

So then why can the Gravitational field escape the BH? Some how the source of the G field inside the BH is communicating with the mass or energy outside the BH to tell it to curve into the BH.

 

[pervect]

Try http://www.desy.de/user/projects/Physics/Relativity/BlackHoles/black_gravity.html

"How does the gravity get out of the black hole?"

 

[cragar]

If I read that article correctly. "How does the gravity get out of the black hole?" Then it seems that the G field of the BH is created from the matter right before it goes into the BH . Like it freezes its field in place. Or do i have it wrong?

 

[Q-reeus]

If I read that article correctly. "How does the gravity get out of the black hole?" Then it seems that the G field of the BH is created from the matter right before it goes into the BH . Like it freezes its field in place. Or do i have it wrong?

In #13 I was careful to phrase it "..at least according to the standard BH scenario." what followed was simply a brief account of the orthodox view, I think. There are imo severe difficulties with the very notion of BH. In GR gravitational field is not a source of gravity itself, even though it has a somewhat ill-defined energy density. Which means matter (non-gravitational energy-momentum & pressure) alone is source, and especially if one takes the 'river model' seriously (space itself is falling in at the EH at light speed - see eg http://arxiv.org/abs/gr-qc/0411060), communication from 'in there' to 'out there' seems highly problematic. The link supplied by pervect in #15 offers an explanation of sorts, but not one I personally buy. There are rival theories of gravity where gravity gravitates and a BH never forms, but these are considered fringe theories, so won't refer to any here. But since charged BH's are allowed in GR, it's worth asking how a charge residing at or 'inside' the BH EH is supposed to communicate it's presence to the outside world. From the link supplied in #15:
"Nevertheless, the question in this form is still worth asking, because black holes can have static electric fields, and we know that these may be described in terms of virtual photons. So how do the virtual photons get out of the event horizon? Well, for one thing, they can come from the charged matter prior to collapse, just like classical effects. In addition, however, virtual particles aren't confined to the interiors of light cones: they can go faster than light! Consequently the event horizon, which is really just a surface that moves at the speed of light, presents no barrier."

Can't say that hand-wavy argument particularly satisfies me. Relative to the outside, the charge is a totally frozen entity. Whence therefore is there any possibility of 'virtual particle exchange' when the trapped charge's internal machinery has ground to a complete stop? Maybe an expert on GR here would care to answer that.

 

[pervect]

If I read that article correctly. "How does the gravity get out of the black hole?" Then it seems that the G field of the BH is created from the matter right before it goes into the BH . Like it freezes its field in place. Or do i have it wrong?

On the classical level, it's saying more that the field doesn't have to get out, I think.

The sense in which "nothing can get out of a black hole" is the sense in which if you make a disturbance in the field, the disturbance won't propagate beyond the event horizon. The field itself exists everywhere, it doesn't need to "get out". So if you look at the information point of view, the information about what went in is stored in the field, and it doesn't need to get out. Information about what happens inside the black hole sitll won't get out.

 

[cragar]

On the classical level, it's saying more that the field doesn't have to get out, I think.

The sense in which "nothing can get out of a black hole" is the sense in which if you make a disturbance in the field, the disturbance won't propagate beyond the event horizon. The field itself exists everywhere, it doesn't need to "get out". So if you look at the information point of view, the information about what went in is stored in the field, and it doesn't need to get out. Information about what happens inside the black hole sitll won't get out.

So then we wouldn't be able to find out if the mass distribution changed inside the BH.

 

[Naty1]

"How does the gravity get out of the black hole?" Then it seems that the G field of the BH is created from the matter right before it goes into the BH . Like it freezes its field in place.

CORRECT.

Leonard Susskind popularized the "stretched horizon" to a densly packed surface of bits (information) just outside the horizon.

So then we wouldn't be able to find out if the mass distribution changed inside the BH.

correct...you can't observe and then report outside the horizon. And you would not see a distribution anyway:


Kip Thorne in BLACK HOLES AND TIME WARPS says:

GR...insists that the mass of stellar matter is concentrated into the miniscule region called the singularity at the holes very center. There should be emptiness out to the horizon except for infalling interstellar gas and the radiation the gas emits...in the singularity the rules of qantum gravity destroy time leaving space alone...

(I'm pretty sure conventional "mass" no longer exists as we know it at the singularity either...for example, how could you observe mass without time??)

He goes on to say that John Wheeler called the singularity quantum foam...but acknowledges that

...we might be on the wrong track in believing that singulairities are made of quantum foam

...because we have no complete theory of quantum gravity.


Leonard Susskind's THE BLACK HOLE WAR has quite a "bit" (pun!) about information on the stretched horizon (just a Planck length outside the usual one)...and why information cannot be extracted from it to the outside world...

The posts immediately prior to this one all agree with what I have read...and Dalespam has no reason to doubt what he posted...

 

[Naty1]

I forgot to mention: Black hole stretched horizons meet the HOLOGRAPHIC PRINCIPLE meaning that all the information within the interior horizon volume is avaiable on the surface. That's discussed by Susskind in the book I mentioned above...He developed the details of that theory which I think Hooft initiated..they worked together...and Hawking adopted...

(which is a pretty crazy theory in its own right...so black hole theories are pretty cool somewhat bringing QM, GR, and string theory together.

 

[pervect]

So then we wouldn't be able to find out if the mass distribution changed inside the BH.

Yes, that's what the "no hair" theorem is about. http://en.wikipedia.org/w/index.php?title=No-hair_theorem&oldid=428477892

The no-hair theorem postulates that all black hole solutions of the Einstein-Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three externally observable classical parameters: mass, electric charge, and angular momentum. All other information (for which "hair" is a metaphor) about the matter which formed a black hole or is falling into it, "disappears" behind the black-hole event horizon and is therefore permanently inaccessible to external observers.

I don't have a better reference than the wiki handy at the moment,but what the wiki says matches up with my recollections. Though I think there may be some "fine print" being omitted, especially if one gets into quantum gravity and such.

I suppose I should point out that the issue of determining "mass distribution" is not precisely solved in GR even outside a black hole, ,but I'm not sure I want to get into any great detail. So I'll just mention that it's not as open-and-shut as it is in Newtonian theory.

GR does does define the stress-energy tensor, which is the source of the gravittional field in the theory,but defining "mass" as a familiar scalar quantity has some issues.