Hawking has theorized that there would be "information loss" in black hole singularities based on predictive calculations of GR. I'm trying to understand his theory in laymen terms, and here's what I have right now:

As a star collapses, there are two unique events that predict that there is a loss of "information" (as opposed to energy, which I do not believe is relevant to this situation). The first occurs when the collapse reaches a point where photons can no longer escape, the event horizon. At that point, an observer would no longer be able to discern through any means the chemical composition of the star. spectography is based on light, whether visible or not. So, if no light, no ability to discern any further the makeup of the star. This is the first loss of information.

As the collapse continues towards radius = 0 (singularity predicted by GR), the actual atomic structures of elements begin to cram together to such a point that even if there previously were "elements" within the collapsing star, they ultimately lose their identity as the atoms lose their unique structures. This loss of information is complete loss.

This leads me to believe then that chemical composition of a star has absolutely no bearing on whether it can become a black hole. It all comes down to mass and angular momentum. (I think there is something else as well, but I can't remember it. Might be "G" - whatever that is).

If I understand what he is leading to here, the problem becomes very fundamental. If there is information loss of any sort, let alone 100% loss at radius = 0, then matter has technically been destroyed. The way he states it, while the star can be observed through it's destruction, one cannot work from a singularity back to the star.

Am I on track here?

<font size=-1>[ This Message was edited by: DJ on 2002-02-14 09:51 ]</font>

<font size=-1>[ This Message was edited by: DJ on 2002-02-14 11:04 ]</font>

Sounds about right. If you find a previously undiscovered black hole, you cannot directly know its history.

However, we can make deductions. We do know how some black holes can form (life stage of large stars, etc.) so if you see a 4-stellar mass black hole, it's a good bet that it used to be a star. If you find a million stellar mass black hole, then you know it came from another source because stars can't be that big.

In "A Brief History of Time", Hawking put it as "a black hole has no hair" meaning that a BH can be totally described by its mass, angular momentum and charge. What went in to it is irrelevent. The make-up of the Hawking radiation of an evaporating black hole is unrelated to the composition of the original mass that went into it.

__________________
Any day you wake up on "the right side of the dirt" is a good day.

T. Anderson

That's it! Electric Charge. But to say what went into it is irrelevant - is irresponsible! It is not irrelevant, it's irretrievable. Irregardless, the fundamental problem does exist.

<font size=-1>[ This Message was edited by: DJ on 2002-02-14 15:33 ]</font>

What I meant was that as long as the ratio of positive to negative charges is right, the mass (or mass equivalent in the case of photons) is right and angular momentum is the same the black hole will be identical to any other black hole with the same three parameters. Maybe you use a different definition of irrelevent. [img]/phpBB/images/smiles/icon_smile.gif[/img]

__________________
Any day you wake up on "the right side of the dirt" is a good day.

T. Anderson

"As the collapse continues towards radius = 0 (singularity predicted by GR)..."

I'm neither so learned nor so mathematically skilled as most of you guys, so bear with me if you can. In my intuitional way of thinking about black holes and spacetime curvature, I had envisioned the circumference of the collapsing star going toward zero whilst the radius goes toward infinity. Due to the curvature, don't you see? And then when the whole shebang reaches the Planck scale something happens that we can't see clearly just yet due to the limitations of our theories.

(This doesn't have too much to do with the information paradox, but it's been bugging me. Can ya set me straight please?)

--Don Stahl

You are on the right track. The cicumference shrinks to the Schwartzchild limit (event horizon). The Schwartzchild radius is this cicumference/2pi. Technically, it is measured from the outside. The radius of the event horizon (as measured from the inside) is infinite.

<font size=-1>[ This Message was edited by: Kaptain K on 2002-02-14 16:24 ]</font>

The information loss problem is a "problem", because it requires a transformation of states that is not allowed by quantum mechanics. I won't try to paraphrase the details, but I will give a couple of links you can follow, which may or may not help.

<ul>[*]Black Hole Information Loss (from the Usenet Physics FAQ).[*]The Black Hole Information Paradox, a lecture by Finn Larsen, of the Enrico Fermi Institute.[/list]

Thought about this then recalled and found the following: (The Nature of Space and Time, Hawking & Penrose, Chap. 1, P. 12)

Hawking: One normally thinks of a spacetime singularity as a region in which the curvature becomes unboundedly large. However, the trouble with that as a definition is that one could simply leave out the singularity points and say that the remaining manifold was the whole of spacetime. It is therefore better to define spacetime as the maximal manifold on which the metric is suitably smooth. One can then recognize the occurrence of singularities by the existence of incomplete geodesics that cannot be extended to infinite values of the affine parameter. Inset: Definition of Singularity. A spacetime is singular if it is timelike or null geodesically incomplete but cannot be embedded in a larger spacetime.


I'm taking it that the radius cannot be infinite.

However, several of the diagrams later in the text refer to radius=0, but perhaps because Hawking and Penrose are trying to display 4-dimensional properties in 2 dimensions.

DJ

<font size=-1>[ This Message was edited by: DJ on 2002-02-16 09:04 ]</font>

Ouch. Is there some context that would help explain this quote from Hawking & Penrose to my unprepared mind? How do they define a "suitably smooth" metric, for instance?

Is this saying that we define the spacetime metric to be everything for which the curvature does not exceed [upmty-ump], and we recognize a spacetime as singular if the curvature exceeds [umpty-ump]? If so, how do we arrive at [umpty-ump]?

--Don Stahl

<font size=-1>[ This Message was edited by: DStahl on 2002-02-16 15:57 ]</font>

Now you're exactly where I am. [img]/phpBB/images/smiles/icon_smile.gif[/img]

I think part of the problem is that if inside the black hole, it would appear infinitely large, but to the outside, it appears to approach 0.

Thus, infinity = 0 in this case. Quite the paradox, and part of what I perceive the actual problem is.

It may be of interest to note that not all experts agreee that the "information loss" is as total or pervasive as is often presented in popular accounts. See for example Lectures On Black Hole Evaporation and Information Loss by Thomas Banks from Rutgers, the abstract of which notes in part that

<BLOCKQUOTE>". . . information can be lost to the original asymptotic observer without violating the rules of quantum mechanics, because a black hole remnant is viewed as a large space connected onto our own by an almost pointlike opening. It does not behave like an elementary particle. Objections to remnants are refuted and the (remote) possibility of testing this scenario experimentally is discussed. Also included is a brief description of Susskind's picture of the stringy origin of Bekenstein-Hawking entropy. An attempt is made to argue that the cornucopion picture and Susskind's model of the states responsible for black hole entropy are compatible with each other. Information is lost to the asymptotic observer in Hawking evaporation, but the information encoded in the BH entropy remains in causal contact with him and is re-emitted with the Hawking radiation."</BLOCKQUOTE>

I'll need to study more thoroughly what you've presented. One thing I did note was the description of a seperate time segment outside of traditional spacetime, or something like that. That definition would make it non-singular by the definition presented above. I think. [img]/phpBB/images/smiles/icon_wink.gif[/img]