Why do blackholes cut off from the rest of the universe

[g.lemaitre]

This is from Hawking's Brief History of Time:

it seems that gravity may provide a limit to this sequence of “boxes within boxes.” If one had a particle with an energy above what is called the Planck energy 10 to the 19 electron volts, its mass would be so concentrated that it would cut itself off from the rest of the universe and form a little black hole.

I don't see why the black hole is cut off from the rest of the universe. The black hole is still there and it's still made of ordinary matter, just a more dense than other matter. Is it because time stops in a black hole? Or that nothing can escape from it? Even if those two traits are true I don't see why those conditions qualify as cutting one's self off from the rest of the universe.

 

[Mark M]

Since light defines the maximum speed for anything carrying information, and since light cannot escape a black hole, nothing can escape a black hole. Nothing inside the black hole can directly have an effect on something outside the black hole.

 

[PeterDonis]

The black hole is still there and it's still made of ordinary matter, just a more dense than other matter.

The black hole is not made of ordinary matter; the ordinary matter that originally collapsed to form the black hole falls into the center at r = 0, forms a singularity there, and disappears. The black hole itself is entirely spacetime curvature; there is no matter anywhere (i.e., the stress-energy tensor is zero).

That said, I'm not sure that "cut off from the rest of the universe" is the best choice of words. Objects can still fall *into* the hole; but once inside, nothing can escape *out* of the hole.

 

[Muphrid]

As a point of interest, there are Einstein-Cartan theories that replicate GR well with torsion hand set to zero, and in those, the stress-energy tensor of a black hole is a delta function at the singularity.

 

[PeterDonis]

As a point of interest, there are Einstein-Cartan theories that replicate GR well with torsion hand set to zero, and in those, the stress-energy tensor of a black hole is a delta function at the singularity.

Can you give a reference for this?

 

[Muphrid]

See http://arxiv.org/abs/gr-qc/0405033. While the authors' derivation of various spherically symmetric spacetimes begins with section 6, the part about what the stress energy tensor is for a black hole isn't discussed until page 64. Admittedly, most of the math is wrapped up in their geometric algebra formalism--if you're familiar with tetrads and the Ricci rotation coefficients, it might not be too alien, but some stuff from exterior algebra (particularly about bivectors) would be helpful, too. There's another paper by Hestenes that tries to hew a little more closely to traditional index notation, but the differences are somewhat slight.

At any rate, I will admit it's unclear to me how exactly this formalism differs from GR to the point that it can say something meaningful about the stress energy tensor at the singularity where GR cannot (and not just that, but for rotating black holes, too). The authors themselves seem to think this could be a means of testing the difference between traditional GR and their mathematical description.

Edit: appendix C can also give a quick and dirty translation from tensor calculus to the geometric algebra description of gravity.

 

[PeterDonis]

See http://arxiv.org/abs/gr-qc/0405033.

On a quick skim, this seems very interesting; I'll take a more detailed look when I have time. I see what you mean about their SET for a black hole; they specifically describe it as a "point source" at the origin. Their model appears to make all the same predictions about the horizon, though (i.e, that nothing can escape out of it).

 

[Naty1]

I don't see why the black hole is cut off from the rest of the universe. The black hole is still there and it's still made of ordinary matter, just a more dense than other matter. Is it because time stops in a black hole?

In a real sense, nobody REALLY understands the horizon of a black hole...but as already noted science does have some explanations. Try Wikipedia on COSMIC CENSORSHIP HYPOTHESIS as a start. And if that is not weird enough, wait til you discover that everytime an observer accelerates, a horizon forms: and that has other remarkable implications:. Even in cosmology, the study of the entire universe!

Time does not stop inside a black hole and in fact for a free falling observer, one just drifting, there is no black hole horizon. But things get really interesting when one tries to remain stationary, to hover, outside a black hole horizon...via acceleration...then the black hole horizon appears and it's radiation frys the observer. And there appears to be a singularity in time at the horizon...that is, time really slows down more and more the closer you get when hovering.

A really interesting book on the subject is THE BLACK HOLE WAR by Leonard Susskind...very little math, some string theory and 'complementarity' descriptions for us laymen, many other fascinating descriptions and insights about his decades long disagreements with Stephen Hawking. Their fundamental disagreement was whether information [of everything that falls into a black hole] is really 'cut off' from us; turns out Susskind was right and Hawking eventually conceded.

In fact here is a discussion you might like
https://www.physicsforums.com/showthread.php?t=553366
It starts out with a particle discussion...one of those 'implications' of horizons to which I referred.

 

[g.lemaitre]

The black hole is not made of ordinary matter; the ordinary matter that originally collapsed to form the black hole falls into the center at r = 0, forms a singularity there, and disappears. The black hole itself is entirely spacetime curvature; there is no matter anywhere (i.e., the stress-energy tensor is zero).

Is this really true? I have a hard time believing this. There has to be something inside the Schwarzschild radius, otherwise it wouldn't have any effects. nothing causes nothing. I have trouble believing that 100% spacetime curvature is nothing. Later, I'll try to find some passages that describe what's inside the Schwarzschild radius.

 

[PeterDonis]

Is this really true? I have a hard time believing this.

In the case of an "eternal" black hole, one that exists forever (the "maximally extended Schwarzschild spacetime"), the SET is zero everywhere in the spacetime. However, as far as I know nobody believes that this solution is physically reasonable.

In the case of a physically reasonable solution, where a massive body collapses to form a black hole, the SET is nonzero inside the massive body, so it is not zero everywhere in the spacetime. There is a portion of the spacetime where the massive body is still present (and therefore the SET is not zero) inside the horizon, as it collapses to the center at r = 0 and forms a singularity there. But after the singularity forms, there really is nothing inside the hole--the SET is zero everywhere.

There has to be something inside the Schwarzschild radius, otherwise it wouldn't have any effects. nothing causes nothing. I have trouble believing that 100% spacetime curvature is nothing.

You're right; it isn't "nothing". It's spacetime curvature. But it is not "ordinary matter". The only "ordinary matter" is inside the massive body that collapses to form the hole; and that isn't there any longer once the singularity forms.

 

[Naty1]

Originally Posted by PeterDonis

The black hole is not made of ordinary matter... there is no matter anywhere (i.e., the stress-energy tensor is zero).

Is this really true?

seems to be so...and it happens in a finite time...

One way to look at it is to observe a black hole WAS made of real matter. But it supposedly disappears at the singularity while it's effects remain 'on the horizon'.

Here are a some explanatory quotes I like:

the past light cone of the infalling mass is the source of the external field.

Marcus:

When very compressed, the distinction between matter and space {and time} disappears and one gets down to a stew of microscopic degrees of freedom, which we don't yet know how to model mathematically.

Mitchell Porter [our forum] posts:

... the idea is that the interior of the black hole has a dual (holographic) description in terms of states on the horizon; a lot like AdS/CFT, with the horizon being the boundary to the interior. So when someone crosses the horizon from outside, there's a description which involves them continuing to fall inwards, until they are torn apart by tidal forces and their degrees of freedom redistributed among the black hole's degrees of freedom, all of which will later leak away via Hawking radiation; but there's another description in which, when you arrive at the horizon, your degrees of freedom get holographically smeared across it, once again mingling with all the black hole's prior degrees of freedom (also located on the horizon), which all eventually leak away as Hawking radiation

Kip Thorne:

...the freezing of the implosion as observed from far away with (in contrast to) the continued implosion as observed from the stars surface...an imploding star really does shrink through the critical circumference without hesitation...That it appears to freeze as seen from far away is an illusion...General relativity insists that the star's matter will be crunched out of existence in the singularity at the center of the black...

Leonard Susskind: [THE BLACK HOLE WAR]

(p258) From an outside observer’s point of view, an in falling particle gets blasted apart….ionized….at the stretched horizon…before the particle crosses the event horizon. At maybe 100,000 degrees it has a short wavelength and any detection attempt will ionize it or not detect it!

(p270)…. eventually the particle image is blurred as it is smeared over the stretched horizon and….and the image may (later?) be recovered in long wavelength Hawking radiation.

Roger Penrose:

There is no mass as we know it (inside); inside all particles have been destroyed and gravitational effects remain outside the event horizon along with a few characteristics (electric charge, spin, etc).

There is no mass as we know it (inside); inside all particles have been destroyed and gravitational effects remain outside the event horizon along with a few characteristics (electric charge, spin, etc).

Personal comment: As much as I like these insights into current theory, I have my doubts about their accuracy. I don't think there is any theoretical nor experimental evidence that density is infinite in a black hole. Nor at the big bang: We simply don't have any theory for these singularities. Nobody knows what happens at those entities: I believe that awaits a complete theory of quantum gravity. The above descriptions, I believe, represent different viewpoints based on different models, different coordinates...for example:

JesseM:

There's no coordinate-independent way to define the amount of time dilation for a clock at various distances from the horizon--what we're talking about is the rate a clock is ticking relative to coordinate time, so even if that rate approaches zero in Schwarzschild coordinates which are the most common ones to use for a nonrotating black hole, in a different coordinate system like Kruskal-Szekeres coordinates it wouldn't approach zero at the horizon at all.

and here's a doozy from Susskind [BLACK HOLE WAR]via Holographic [ADS/CFT] principles:

Holographic Principle (299): Everything inside a region of space can be described by information bits restricted to the boundary. The world is pixilated! The maximum number of bits of information that can fit in a region of space is equal to the number of Planck sized pixels that can be packed on the area boundary…a hologram. (304) The question of where a particular bit of information is located does not have a unique answer. Each successively larger boundary includes all the previous information until we come to the boundary of the universe or infinity….ordinary Quantum mechanics makes an object’s location slightly uncertain; the holographic principle means every time we seek the location of information on the hologram it’s always out at the next level!
(3050 The hologram flickers and shimmers with the uncertainty of a quantum system in order that the three dimensional image have quantum jitters.

 

[PeterDonis]

The black hole is not made of ordinary matter... there is no matter anywhere (i.e., the stress-energy tensor is zero).

Is this really true?

Classically, yes. All the quotes you gave that seem to say otherwise are referring to proposed quantum corrections to the classical behavior. See further comments below.

One way to look at it is to observe a black hole WAS made of real matter. But it supposedly disappears at the singularity while it's effects remain 'on the horizon'.

Actually, the "effects" of the matter remain throughout the spacetime, since they include gravity--spacetime curvature.

I don't think there is any theoretical nor experimental evidence that density is infinite in a black hole. Nor at the big bang: We simply don't have any theory for these singularities. Nobody knows what happens at those entities: I believe that awaits a complete theory of quantum gravity.

I agree.

The above descriptions, I believe, represent different viewpoints based on different models, different coordinates

Not just "different coordinates"--the differences that are being referred to are actual differences in *observations*. For example, Susskind in The Black Hole War (which I'm just re-reading now, as it happens) talks about the extreme difference in what infalling observers see at the horizon (nothing special) vs. what "hovering" observers see (a hot "atmosphere" of particles, some of which get emitted as Hawking radiation). So these two observers would differ about "what the black hole was made of", at least at the horizon--one observer sees nothing, the other sees a hot thermal bath of particles.

(One thing that I haven't seen talked about, though, is this: what is the SET of the hot thermal bath of particles? Since some get emitted as Hawking radiation, which can be detected "at infinity", it doesn't seem that that SET can be zero.)

[Edit: removed statement at end]

 

[jcsd]

(One thing that I haven't seen talked about, though, is this: what is the SET of the hot thermal bath of particles? Since some get emitted as Hawking radiation, which can be detected "at infinity", it doesn't seem that that SET can be zero.)

As you rightly point out it there's a positive energy flux at infinity, but there's also a negatuve energy flux into the black hole (whence black hole evaporation). as being the stress-energy of a quantum field it doesn't need to satisfy classical energy conditions. Wald covers it briefly, mentioning this paper: http://prd.aps.org/abstract/PRD/v21/i8/p2185_1

 

[PeterDonis]

being the stress-energy of a quantum field it doesn't need to satisfy classical energy conditions.

Yes. But the fact that there is a quantum field there at all means the SET is not zero, as it is in the classical Schwarzschild black hole solution.

Googling uncovered an abstract of another article that appears to actually describe the SET of the Unruh vacuum state, which seems to be the best candidate for the "SET of the quantum field around a black hole". Unfortunately that paper, and the one you linked to, are behind a paywall so I can't access them.

 

[jcsd]

Yes. But the fact that there is a quantum field there at all means the SET is not zero, as it is in the classical Schwarzschild black hole solution.

Yes, though really as it's a quantum field it's the expectation value of the stress energy tensor that we're seeking to find. That's where black hole evaporation comes from: measuring the back reaction of the quantum field on the black hole and making a few seemingly reasoanble assumptions.

Googling uncovered an abstract of another article that appears to actually describe the SET of the Unruh vacuum state, which seems to be the best candidate for the "SET of the quantum field around a black hole". Unfortunately that paper, and the one you linked to, are behind a paywall so I can't access them.

This is probably the paper you want (not behind a paywall either): http://projecteuclid.org/DPubS/Repo...d.cmp/1103922593&view=body&content-type=pdf_1