black hole singularities

[dstebbins]

I was just read through Stephen Hawking's best selling book A Brief History of Time, and he continuously made comments about how a star experiencing gravitational collapse would eventually collapse to form a point of infinite density.

 

Wait: Infinite density? If it's possible for a star to become infinitely dense, then it should also be possible for an object to accelerate to c, giving itself infinite mass. If infinity is obtainable in one way, then it must be obtainable in another.

 

The explanation for mass not becoming infinite, however, is that if energy is continually applied to it, it will go faster and faster, but its rate of acceleration, if you will, will start to go down as it approaches c, so if you graph an objects mass relative to its velocity on an xy coordinate grid, with the object's rest mass being at 1, then c will be an asymtope (spelling?).

 

So why can't we say the same about black hole singularities? Why can't we say that, as a star experiences gravitational collapse, it will get smaller and smaller at the rate of m=Xvt, where m is the mass of the star experiencing gravitational collapse, v is the volume of the star/black hole, t is the time that has elapsed since the gravitational collapse began, and X is the "singularity constant" if you will (I chose X because I like the letter X), with a unit of kg/(sm^3). By this theory, only after an infinite amount of time, which is never reached, does the volume equal zero, and density become infinite.

 

Now, I know what some of you are thinking. "That would mean the event horizon would continually expand because the gravity is increasing." Keep in mind that this is relativity we're talking about (it was relativity that invented the concept of black holes), and relativity provides for spacetime curvature/distortion. It's possible that, after a while, the gravity of the star/black hole becomes so powerful that spacetime is becoming distorted at the rate at which gravity is increasing, so relative to a person a safe distance from the event horizon, those two things exactly cancel each other. This particular fix might require a slight modification to Einstein's theory of gravity so that it becomes a little more powerful at black hole levels, but hey, scientific laws are being rewritten all the time, so this should be just a drop in the bucket for scientists.

 

I'm pretty sure this has been thought of before (black holes aren't one of those things that can be solved by a "why didn't I think of that" answer), so where am I going wrong?

[BenTheMan]

So why can't we say the same about black hole singularities?

 

They're a feature of the classical theory---there's nothing that prevents this from happening. The gravitational forces overcome the other forces acting, to cause collapse.

 

Conversely, it takes an infinite amount of energy to accelerate a massive particle from the speed of light---because you can't FIND an infinite amount of energy in the universe, this is impossible.

 

By this theory, only after an infinite amount of time, which is never reached, does the volume equal zero, and density become infinite.

 

You have to be careful to include GR effects here. Your argument is invalid when gravity starts becoming stronger. Also, you have no way do derive `X'. What you have said is (essentially) what happens for an observer at infinity. An observer nearby will watch the star collapse and see a black hole form in finite time.

 

It's possible that, after a while, the gravity of the star/black hole becomes so powerful that spacetime is becoming distorted at the rate at which gravity is increasing, so relative to a person a safe distance from the event horizon, those two things exactly cancel each other.

 

You have to SHOW this, you can't just SAY it

 

This particular fix might require a slight modification to Einstein's theory of gravity so that it becomes a little more powerful at black hole levels, but hey, scientific laws are being rewritten all the time, so this should be just a drop in the bucket for scientists.

 

That's being pretty cavalier... ``Modify gravity! I mean, everyone ELSE is doing it.''

[ajb]

I agree with Ben,

 

in the context of general relativity it has been shown by Hawking and Penrose (and other I imagine) that a singularity must form when a massive object collapses. It appears to be a very generic feature of general relativity.

[BenTheMan]

I agree with Ben,

 

I always get sucked into black hole threads (HA!), even though my GR is weak. No one ever wants to talk about SO(10). I'm glad you agree

[Norman Albers]

Modelling the collapse of a "dust ball" yields an asymptotic solution such as BenTheMan are wrassling with in the Quantum Mechanics thread. However the time constant is the Schwarschild radius divided by the speed of light, so maybe 10^-4. As Ben points out, the theory reaches its own limit, like a guide who takes us to the high mountain divide, and then says, I leave you here to find a further guide.

[BenTheMan]

Modelling the collapse of a "dust ball" yields an asymptotic solution such as BenTheMan are wrassling with in the Quantum Mechanics thread.

 

Nonono---for a dustball, or a dying star or something, a black hole forms in finite time, no problem. now if that dust was massless...

[wedge554]

can i add somthing in here that you might find interesting (mainly me theorising but im not an expert in this field so point and shout if im wrong!)

 

I believe what you are on about, especially the "time" ratio to "gravitational mass" ratio. Would it be worth considering that if a black hole (within the hole and not on the rim or outskirts of it) time was not a factor then the black hole could be influenced by our own "time space"? therefore a black hole does not actually exist because nothing apart from some type of radiation (i have forgotten what it is called) can be spat out of one? It only exists because our time space allows it to? Moreover, relating the black holes effects to a hurricane as such where you have the eye of a storm (where there is no momentum or wind, but is effected by the outside of the hurricane spiral) it would relate to the theory that the center of a black hole does not actually contain gravity or known matter, but contains a hole to either different dimensions or a more realistic theory that it is a gate to another part of space not accessible through our form of matter?

 

Sorry if this sounds confusing, i seem to have lots of theories?!

[BenTheMan]

therefore a black hole does not actually exist because nothing apart from some type of radiation (i have forgotten what it is called) can be spat out of one?

 

No, a black hole certainly exists, because an observer can watch an horizon form.

[wedge554]

sorry, what i meant was, a black hole exists in our perception, yet the center of the black hole does not actually exist in relation to our own time space, so it theoretically exists while it doesnt?!

[BenTheMan]

yet the center of the black hole does not actually exist in relation to our own time space,

 

I don't think you can say this. I think that the singularity forms classically---whatever quantum theory of gravity you want should prevent the singularity from forming, but classically you are stuck with it.

[wedge554]

i dont really know what you mean by quantum gravity, but im assuming you mean gravity formed by dark matter which is in relation to the black hole on the other side of the black hole? - i would really like to read in to this, but i dont have the time i read too many books already lol.

[BenTheMan]

Well, quantum gravity is a general term for a quantum description of gravitational phenomena. For example, the singularity occurs in the classical theory when a star collapses---that is, there is nothing to prohibit the matter from collapsing all the way to zero size, which is how you get a singularity.

 

But we expect that there some new physics which prevents the singularity from forming---this is the catch-all phrase ``quantum gravity''.

[Norman Albers]

No, a black hole certainly exists, because an observer can watch an horizon form.

My textbook says "One would see the surface falling freely in precisely the same menner as the test particle discussed, that is, it would shrink asymptotically toward radius 2m."

 

I found the other relevant quote: "When the necessary light nuclei have been used up, the fusion process ceases, the stellar equilibrium cannot be maintained, and in some cases the gravitational force collapses the star, shrinking it to a size asymptotically approaching its Schwarzschild radius. Thus for radii slightly greater than 2m and times that are finite the geometry becomes that which we have discussed: the asymptotically collapsing start would appear as a black hole." Curiouser and curiouser.

[BenTheMan]

Ugh. Ok I give up... I'll stick to particle physics

[Norman Albers]

"...gonna make a mess outta you." Bob Dylan Take heart, it looks like a black hole!

[Martin]

I was just read through Stephen Hawking's best selling book A Brief History of Time, and he continuously made comments about how a star experiencing gravitational collapse would eventually collapse to form a point of infinite density.

 

Wait: Infinite density? ... This particular fix might require a slight modification to Einstein's theory of gravity so that it becomes a little more powerful at black hole levels, but hey, scientific laws are being rewritten all the time, so this should be just a drop in the bucket for scientists.

 

Stebbins may have lost interest in thread and de-subscribed. I'll reply to the original post anyway just in case he's still around.

 

Stebbins my compliments on having good intuition. Tendency is for leading QG researchers to do exactly that, MODIFY gen. rel. so that nonsense like "infinite density" is avoided, improved theory reproduces classical results in classical regime but does not break down. You basic hunch about that is right.

 

However before getting into it with own notions it's a good idea to look around to see what the bigleague is thinking and talking about this business of getting rid of (or "resolving") singularities.

 

So I would advise scanning, sampling maybe, this

http://online.itp.ucsb.edu/online/singular_m07/

 

Three week January 2007 workshop at Santa Barbara on resolving singularities (mainly the black hole and big bang)

Participants included Loop Quantum Cosmology stars and some bigname Stringers (David Gross, Steve Shenker, Gary Horowitz, Steve Giddings, Robert Brandenberger, many others.)

Gross was there some although not on the official list----it is his Institute (he is the director of KITP)

 

I am not suggesting that we should respect people simply because the are famous, or that they are to be believed simply because they are world class top people in some field (Loop Quantum Cosmology, or String, or whatever). what I'm saying is that our tax dollars support these guys and it is at least reassuring to know that a good many of them are trying to do the same thing as you were attempting in your orig. post, which is to somehow get rid of the singularity in the black hole

 

The LQC people have so far made better progress with getting rid of the Bang singularity. the key thing is without their putting it in by hand, when they quantize standard cosmology some quantum "corrections" appear at very high density with the effect that gravity becomes repulsive at density up near Planck density and collapse seems to reach a limit----density does not become infinite---so the theory does not break down like GR does. Computer models using LQC equation characteristically show a bounce at around Planck density. We've discussed this in other threads, but you may have missed it. Similar conclusions may arise in the black hole case but the work there is more preliminary---only a few papers on it so far and little or no computer simulation so far. That is just a sample. If curious you can check out the video of Ashtekar's and Bojowald's talks at the KITP January workshop.

[Norman Albers]

Nice, Martin. This is a very high continental divide, and I take it as a very good sign that I end up talking relativity in the QM section and a little quantum nature in the relativity section. This is where I am working.

[Martin]

Nice, Martin. This is a very high continental divide, and I take it as a very good sign that I end up talking relativity in the QM section and a little quantum nature in the relativity section. This is where I am working.

 

Thanks Norman! I'm sorry Stebbins seems to have gotten fed up and left the thread but I'm glad you found something useful in my post along with the rest.

[lakmilis]

I still would say that the textbook perhaps errs a little in saying a star collapses to the Schwarzchild radius... is it a 1st year university physics book or similar? They all tend to use classical escape velocity to derive this radius and don't even mention that this is not a valid method nor accurate? And for the hell of it, special relativity would predict R= GM/c^2 , thus half the product (although SR isn't valid either) for this. In GR star collapses are more correctly given a correct R by the Kerr metric.

[CanadaAotS]

I'm running out of time here, so I've only read the first post, but infinite density just happens to be an ugly little side effect of our current understanding of black holes. It's just that we know of no physical construct that could resist the pressure that gravity is creating inside the event horizon of a black hole... because we can't take a look around the inside of the horizon and report back, as far as we know all the mass that enters a black hole is crushed into a single point, a la singularity.

 

That's my 2 cents, time to run for my next class.

[Royston]

as far as we know all the mass that enters a black hole is crushed into a single point, a la singularity.

 

I'm not sure that's correct, I don't think a black hole singularity becomes a single point, anymore than [math]\frac{a}{0}[/math] [math][0,\infty][/math] becomes a single point, it's just infinite, and therefore (in this context) non-physical.

[Fred56]

Don't quote me on this, but I can remember reading something about Albert being initially skeptical of black holes and how they are supposed to form. Because the infalling or contracting matter must necessarily exceed the speed of light, which would require infinite energy, according to his equations, he postulated that matter would not fall beyond the radius, but stop, or freeze, or something. But apparently that matter just keeps on going towards the centre, past the radius and into the singularity, smacckkk...! ...or something.

 

My take on black holes is that if matter has fallen beyond some radius that requires infinite energy, or exceeding the velocity of light, then perhaps it already is a singularity and so beyond known Physics.

[ajb]

It is wrong to think of a singularity as being a point in space-time. Technically, as "at" the singularity the field equations break down you have to remove this point so that you have a well defined theory. Singularities then manifest themselves as geodesic incompleteness, that is some geodesics "fall off" the manifold. So Snail is correct, even if he didn't realise it!

 

 

 

Fred56 raises an interesting point which we have all discussed before. Albert Einstein died before Hawking and Penrose formulated their singularity theorems and related ideas. Since Einstein, we have formulated what we shall call "modern geometry and topology" in the 1960's and after. So, although Einstein was the first to propose general relativity we now have much more powerful tools in which to study it. As such, you cannot take Einstein's ideas as proven or worth any more investigation than any other person working on general relativity. Einstein is not some "god" that we all worship, but he is the farther of a lot of modern physics.