Scwarzchild radius

[Fred56]

Black hole formation is like a gravitational collapse which creates a point of infinite density which “consumes” the matter within the (Scwarzchild) radius, or it forms an asymptotic distribution of some sort...? Could it be viewed as some kind of relaxation of a manifold (that undergoes a phase inversion, or somehow leads to a restriction of degrees of freedom)? Or have I got my Scwarzchild r's about phase altogether?

[Martin]

In General Relativity black hole formation leads to infinite density.

This is one way of showing that GR fails to cover that case----it breaks down in that case because it predicts something without physical meaning.

 

So people are developing a replacement that won't break down, and will not have "singularities." (Singularities are places where a manmade theory breaks down, gives meaningless results, and stops corresponding to nature. They represent limits to applicability.)

 

A recent paper about this was by Kevin Vandersloot, a young American physicist who is currently in Portsmouth UK---there is an institute there for gravitation and cosmology research. Another to keep an eye out for is Christian Boehmer. An Italian physicist named Leonardo Modesto has been working on this for several years. Martin Bojowald has written about this recently as well.

One way to find their papers, to get an idea of what is going on, is to put the author's name into the search engine at arxiv.org.

 

To date there is no popularization writing about this, as far as I know.

[Fred56]

I've read some Bojowald, but it's hard to follow.

[Martin]

I just checked at Google.

If you put in

Kevin Vandersloot Christian Boehmer

then Google gives you their September 2007 paper on the

Schwarzschild interior.

 

It doesnt get much better!

You are asking about the Schwarzschild interior.

That is exactly the topic they are writing about.

They posted a new research paper just last month!

 

Maybe you will find their paper easier to understand than what you read of Bojowald. Or maybe you won't. It is new research and there has been, to date, no popular writing.

 

Here's a link to the Vandersloot Boehmer paper that I got by google just with their names

http://front.math.ucdavis.edu/0709.2129

I see that the paper has already been accepted for publication by Physical Review (series D). They just posted preprint last month. Good place to publish. The field is hot!

 

I am curious. What Bojowald paper did you read? Could you give me a link to it? He has written several different papers on the black hole interior and I'm wondering which one it was that you looked at.

[Fred56]

Do you understand the loop-quantum gravity model?

[Martin]

Do you understand the loop-quantum gravity model?

 

which one? Non-string QG is a fast growing rapidly changing field---there are a lot of different competing models being worked on.

 

I understand some of the models to some extent---perhaps in certain cases more than you do, because of having studied them more. So I could try to explain. And there would of course be gaps---things I could not adequately explain. If you have some Loop paper (or spinfoam, or CDT...one of those approaches) give me the link to it and, if I like the paper I will see if I can help you understand. There is no one single nonstring QG model, or approach, so the efficient way is to designate a paper to focus on.

========================

 

Since you were asking about blackholes, I went and looked at the Vandersloot paper. Here is how it starts:

 

INTRODUCTION

 

A long held expectation is that the singularities predicted from general relativity signal a breakdown of the classical theory requiring a more proper accounting of the quantum effects of gravity. The situation is analogous to Hydrogen atom in ordinary mechanics, where classically the electron is expected to in-spiral towards the proton leading to a singularity. This behavior is cured when quantum mechanics is taken into account leading to a stable non-singular Hydrogen atom. In general relativity, two of the most relevant forms of singularities are the big-bang cosmological singularity, as well as black-hole singularities. A central question to be answered by any quantum theory of gravity is whether these singularities are regulated by incorporating quantum effects. Furthermore, if a quantum theory of gravity were to resolve the classical singularities, it would be of paramount interest as to what replaces them dynamically.

 

A leading candidate theory of quantum gravity is known as loop quantum gravity (for reviews see [1–3]). The application of loop quantum gravity techniques to cosmological models is known as loop quantum cosmology [4] which has led to a resolution of the big-bang singularity, replacing it with a big-bounce for homogeneous and isotropic models [5–7]. These results provide tantalizing first hints that loop quantum gravity may indeed provide the singularity resolution hoped for in a quantum theory of gravity. Thus the next step is to consider loop quantum gravity for the black hole scenario.

 

The simplest first step in considering loop quantum black holes consists of examining the interior of a Schwarzschild

black hole. There, the temporal and radial coordinates flip roles, and the interior becomes a Kantowski-Sachs cosmological

model whereby the metric components are homogeneous and only time dependent. The interior therefore can be quantized in a similar fashion as loop quantum cosmology leading to the possibility that the singularity is resolved as in the cosmological case. The loop quantization of the Schwarzschild interior has been initially developed in [8] and [9]. There, the quantization indicates that the quantum Einstein equations are non-singular in a similar way loop quantum cosmology was originally shown to be non-singular [10]. However, the question of what replaces the black hole singularity is not answered.

 

Therefore, we attempt to provide an answer as to what dynamics are predicted from the loop quantization of the

Schwarzschild interior....

[Norman Albers]

Fred, YES! I have been looking at the transverse permittivity in the interior, which is negative, expressed in "external" flat-space coordinates. This implies a real exponent of decay for transverse radiation, leaving only a one-dimensional manifold. Interestingly this effect goes to zero as does radial permittivity which remained positive, toward the origin. Look at my gravitation paper and plot out the two permittivities. You might be seriously amused. Martin, thanks, I'll get with the reference. I just admitted over in the 'gedanken' thread that I am not yet schooled in interpretions of the interior metric. http://www.scienceforums.net/forum/showthread.php?p=364640#post364640 It is easy to say "radial intervals are time-like and time intervals are space-like" but what are we saying, and what are our assumptions about physics? Surprisingly last winter H. Puthoff agreed with me that the concept of proper-time physics is overextended. What gets to happen?

[Martin]

Norman, I would like to suggest that since it is Fred's thread

we first see if we can find a paper that he wants to discuss---and then focus on that paper.

 

If we can find a paper that both he and I like well enough to focus on, I'd be happy to try to explain it. But each of us has a limited range of interest and it is often hard to find an intersection.

 

Let's see what he wants to talk about. If he doesnt have any particular focus then we can broaden the scope.

 

I have suggested the Vandersloot paper to Fred, because it is

1. Peer reviewed and accepted for publication

2. Very recent (last month)

3. About Schwarzschild interior (what he was asking)

4. By a topnotch young researcher---almost no Americans besides Kevin have ever won the prestigeous Marie Curie Fellowship (it is usually only for Europeans).

 

=======================================

 

Well, we waited a decent interval of time I think. Fred didn't take me up on discussing the Vandersloot paper with him.

 

So NORMAN over to you. Sorry for asking you to wait (just wanted to give Fred a chance to decide). Whatever you have that is on topic with Fred's OP.

[Fred56]

Sorry to "keep" you. Just catching some Zs. Here's a snippet from physicsforums:

 

A solution of the Hamiltonian constraint corresponds to a linear combination of black hole states for particular values of the volume or equivalently particular values of the time.

Here's me again:

The singularity has "passed beyond all space and time", it can't “see” the radius, or beyond it. It has passed into some unknown or it is an infinite “distance” from reality? Can you explain what a "volume spectrum" is?

(Bojowald 2000)

It is observed that the stronger the symmetry conditions are the smaller is the volume spectrum, which can be interpreted as level splitting due to broken symmetries. Some implications for quantum cosmology are presented.

[Norman Albers]

Generally we should keep clear on the distinction between event horizon and singularity. I am reading to try to understand the "collapsing dust ball" and interior metric treated as a "truncated Friedman metric". One of the reasons to be amused here is that there is a school of thought where event horizons do not exist distinct from the singularity. These are "dark gray holes" and are the solution of the Einstein field that you get if you do not distinguish the stretching of radial and transverse dimensions as you do setting up the Schwarzschild solution. It's called the isotropic solution (Puthoff wrote on it). So these guys are smiling at the rest of us wondering about interiors. I am trying to understand the relation between proper time and coordinate time. If you accept Schwarzschild physics can you show that the approach to singularity occurs in finite "external" coordinate time? My text shows how, in proper time even on the surface of a collapsing dustball, we go to zero radius in an unceremoniously short time. Does this actually get to happen in finite external time?

[Martin]

Can you explain what a "volume spectrum" is?

 

In quantum mechanics any classical quantity, the result of a measurment, corresponds to a selfadjoint operators on a Hilbert space.

 

The Hilbertspace contains the quantum states of the system and the operator (an "observable") extracts numbers from the states.

 

It is very much like a matrix operating on a finite dimension vectorspace, with usual dot product, that you're doubtless familiar with.

 

I think you know this, it is standard knowledge about quantum mechanics.

 

the new thing is that Quantum Gravity = Quantum GEOMETRY

the Hilbertspace consists of all possible states of the geometry of the universe (or some relevant chunk like a blackhole).

 

Given a geometry, and some material events to serve as landmarks, you can make geometrical measurements----the area of your desktop, the volume of your coffeecup, the angle your computerscreen makes with the desktop.

 

that means that in QG there STATES of geometry and there are geometric observables, or OPERATORS corresponding to area, volume etc. The spectrum of an operator is its set of eigenvalues

 

==========================

 

Fred you indicate you are interested in blackholes. You didnt take me up on Vandersloot's paper. Have you got a link to a recent paper you would like me to look at? By recent, I mean 2005 or later. It is a fastmoving field. You quoted something by Bojowald from 2000. I normally don't go back that far.

 

I'm not sure Bojowald has anything recent about black holes that is suitable for us to discuss. He has been focusing a lot on getting rid of the Big Bang singularity and leaving blackholes for other people. But you could look, here is a list of 60-some papers he has published since beginning of 2003, ordered by number of citations the paper has received in other research.

Check it out you might find something recent about blackhole.

 

http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=a+bojowald+and+date+%3E+2002&FORMAT=WWW&SEQUENCE=citecount%28d%29

[Fred56]

A comment:

My initial post was a speculation, nothing more. I wonder how "valid" a concept it is compared to all the others? So many questions.

Let me rephrase that. How many other models "look" like this? In what way is a black hole an emergent property of the particular “structuring” of its “parts”?

[Norman Albers]

To sum up: when you consider spherically symmetric centrally-sourced fields, in the GR considerations we ask for a bilinear metric and get immediately to the differential expression: [math]ds^2=c^2A®dt^2 - B®dr^2 - C®r^2(d^2\theta +sin^2\theta d^2 \phi) [/math]. We may either proceed allowing B® and C® to be the same (isotropic solution) or allow them to be distinct, whereby we cook up the Schwarzschild solution.

[Fred56]

My intention is to return and complete a grad. qual. I undestand things like a tensor and permittivity, some topology (I have read the SciAm article about fibre bundles over QS several times over and it still hasn't “gone in”). This is really about assessing my ability to understand any model, or what makes it tick. The math can come later. I'm not completely lost but not really at home either. Your'e going to have to go a bit slower for me. I need to understand some terminology a bit better, then there are other things like weekends. Frankly I was surprised I wasn't shot down about some obvious naïve error.

[Norman Albers]

That's cool, Fred, and I also appreciate Martin's statement of us all having different trainings and areas of understanding. General relativity is built up as a four-space mathematics in which changes are assumed to be representable as differentially smooth fields. Thus we always speak of "d - this" and "d-that", since the properties are allowed to change as we go to different placees. The Schwarzschild solution is more general in that we allow different behavior in the radial and transverse senses, the B® and C® above. If you ask for a solution where they are the same, you get "dark gray holes" where there is no outer horizon, just an approach to a singularity.

[scalbers]

Is this a different "naked singularity" mechanism than that briefly mentioned in Wikipedia?

 

http://en.wikipedia.org/wiki/Naked_singularity

[Norman Albers]

Good one, scalbers. I had not heard of this type and it's wild. The rotating source produces a field which has inner singular surfaces in two symmetric polar lobes, and an outer surface also. Because of the rotation the singular surface is not the same as the surface of infinite redshift, but that's not the point here. You are elucidating rotation so strong that these two, inner and outer, shift and merge. Wow! Is there anisotropic opening then, maybe polar? The GR isotropic solution is not the same; there is no singular surface, except maybe at the singularity where your physics sort of falls apart. I don't yet know, however, how angular momentum manifests here.

[pioneer]

Seeds for the imagination

 

One possible way to look at this, is to build a blackhole from scratch instead of looking at it after the fact. Looking at an auto built from scratch on the assemble line, gives one a different feel for the finished product.

 

Say we collapse a star, to give us the needed momemtum/work to form a blackhole. Atomic states will become ionized by the heat as the distances between the nuclei decrease. Relative to atoms what was inside of the atoms, as orbital electrons, comes out as electrons ionize. To form neutron density, what was outside the nuclear composite, i.e., electrons, now needs to come back inside. Based on this cycle, the next step should be the innards of the neutrons coming out, so the neutrons can merge. The final step brings the out, back in, and final particles collapse.

 

When we add matter to a blackhole, the entire out-in-out-in cycle has to replay so the matter can be brought into the collapsing center. Since the distances are so small and the input is continuous, the cycles merge. Say for the sake of argument, we merged the 2 in-to-out cycles and the 2 out-to-in cycles, so the four cyclinder engine, becomes a 2-stroke. In other words, the ionization of the atomic electrons merges with the substructure of neutron density coming outside itself. While the collapse of electrons to form neutrons merges with the final collapse of the matter. Next, we turn the two stroke into a one stroke where both the inside and outside are no longer distinguishable but the matter enters and changes for collapse.

[Mr Skeptic]

Suppose that you had a photon with a wavelength equivalent to the Schwarzchild radius of a mass of equivalent energy. Then

[math]\lambda = \frac{2Gm}{c^2} = \frac{2GE}{c^4} = \frac{2Gfh}{c^4} = \frac{1}{\lambda}\frac{2Gh}{c^3} = \sqrt{\frac{2Gh}{c^3}} = 5.72891594 X 10^{-35} meters[/math]

[math]f = \frac{c}{\lambda} = \sqrt{\frac{c^5}{2Gh}} = 5.23297009 X 10^{42} Hertz[/math]

[math]E = fh = \sqrt{\frac{hc^5}{2G}} = 3.46740157 X 10^9 Joules[/math]

 

Could such an object be a black hole?

 

It would seem like it should be illegal in various respects, what with having a black hole traveling at c, a photon with almost as much energy as a nuke, etc, but I don't see how it would violate a law of physics. Is there anything preventing a photon from having such high energy?

 

Damn! But for the [math]\sqrt{2}[/math], those are Plank units!

 

That can't be a coincidence!

[Norman Albers]

Good clean fun, Mr. Skeptic, I've never seen this presented. I talked with BenTheMan somewhere recently and he thought above maybe 100 GEV photons gave way to heavy bosons and so don't exist as a predominant form. I think the implied frequency of electrons is about 10^21, so this higher energy would have nu of 10^26 or so. I did read something heavy-duty about the gyromagnetic ratio of a black hole...

[Mr Skeptic]

I'm splitting this off to a new thread. Also, I got confused with the reduced planck's constant, so it is actually off by [math]\sqrt{4\pi}[/math] or [math]\sqrt{\pi}[/math]

[Fred56]

Ok, someone on physicsforum's told me this:

Nothing 'consumes' any mass, it's all still there. There is no 'point of infinite density', there is singularity, which has a structure more complicated than just a point. Causal separation happens when you form a 'horizon'.

But the matter is "mapped" differently, right? I mean sure, it isn't eaten by some Laplace demon, but "a more complicated stucture" is more complicated by what "process"? How did it get more "complicated"?