Talk:No-hair theorem

‹See TfM›

Can someone explain the name?

Why is it called "no-hair" theorem or whatever? I can't find any information in the article about the origin of "no-hair" name. 83.10.102.254 (talk) 10:35, 19 February 2009 (UTC)

As it has now been explained as a metaphor, can someone please explain the metaphor?

AIUI (but some anon IP disagreed and reverted) this isn't a metaphor but a simile. We know from simple observation, then a mathematical proof, that it's impossible to smooth down all the hair on an arbitrary "hairy ball" - there's always at least a couple of points where it either sticks up, or is tightly curled. So anything that has "hair" must have such observable points (or boojums). No such points implies that there's no "hair". The simile is to identify something with "hair", and this can be any sort of directed field (i.e. something to which smoothing by orientation can apply). So as we don't observe these points in our theories, we postulate that there's no similar field on the surface of a black hole. Andy Dingley (talk) 16:10, 19 February 2009 (UTC)

is it possible that the word originates with Feynman? rather than being about boojums, it could be referring to the way Feynman thought of topological entities as hairy, green, etc. The explanation for hair seems to be overkill, since accepting that there is no property of hairiness obviates the need to talk about the existence of a property that is implied by hairiness. [fwiw I think it's a metaphor not a simile] Snaxalotl (talk)snaxalotl —Preceding undated comment added 02:01, 11 June 2009 (UTC).

clearly you should put in some more details about the name and what it means...CrocodilesAreForWimps (talk) 21:10, 28 June 2011 (UTC)

Title query

I would like to opine that the title is wrong! The no hair "conjecture", or whatever you want to call it, is not a theorem. A theorem is something you prove. Once you prove it, it is true. The uniqueness theorems are theorems. The only stationary black hole solutions in electro-vacuum Einstein-Maxwell are the the Kerr-Newman class. That's a theorem. Read Heusler's book. You can't have counterexamples to theorems, you can only have examples that have different assumptions. The Einstein-Yang-Mills, Einstein non-minimally couple scalar field etc solutions are counterexamples to the no hair "conjecture" but don't violate the uniqueness theorems. Theorems don't fail by definition (unless someone made a booboo).--Eujin16 (talk) 02:01, 24 March 2008 (UTC)

I think this confusions reflects a confusion in the article. AIUI the NH theorem was made in the context of GR, and within that domain it is pretty well proven, isn't it? cf Price's theorem (no relation) It seems people don't expect the NHT to hold within quantum gravity or a theory of everything; to that extent the so-called counter examples seem rather besides the point. --Michael C. Price ^talk 17:00, 19 February 2009 (UTC)

Language query

This sentence makes no (or very little) sense, but I don't feel qualified to make any amends (First para):

All other information about the matter which formed a black hole or infalling into it, "disappear" behind the black-hole event horizon and are therefore permanently inaccessible to external observers.

First of all, 'information' is singularis, so it should be 'disappears', but 'infalling'? Could someone knowledgeable fix it? Asav 13 Dec. 2005

Igorivanov 14:24, 23 Jul 2004 (UTC) Color is not a pseudo-charge. It is linked to the gauge group, just like the usual charge, so it must be conserved. But, I guess, due to confinement, this is just of academic interest.

"The no-hair theorem postulates" - in my knowledge (and according to the New Oxford American Dictionary embedded in Mac OS X 10.6.7) a theorem is: "a truth established by means of accepted truths", i.e. a result of reasoning. A postulate is "a thing suggested or assumed as true as the basis for reasoning, discussion, or belief". Ouroboros just entered the building. I think "The no-hair theorem states" might be better wording. Sorry, it just bugged me. —Preceding unsigned comment added by 60.236.82.124 (talk) 06:51, 7 May 2011 (UTC)

Microstates and macrostates ?

If the surface of a black hole has entropy S, doesn't that imply that the event surface is in one of (1/k) exp (S) microstates at a microscopic level, just by inverting S = k ln W ?

Why should the fact that its macroscopic properties are determined completely by the no hair theorem worry us any more than any other thermodynamic object which has a well-defined macrostate, but is in an unknown one of many possible microstates ? What is the big problem here ? -- Jheald 22:48, 2 November 2005 (UTC)

I would say there's no problem. Uniqueness theorems have nothing to do with identifying microstates. If they did then the string theorists would be barking mad, which, well, make your own minds up.--Eujin16 (talk) 02:06, 24 March 2008 (UTC)

What about volume?

Since volume doesn't depend on mass, charge, or spin, does the No-Hair Theorem state that black holes have zero volume, or that they all have identical volume, or what? ---63.26.160.105 02:19, 2 February 2006 (UTC)

Well, volume doesn't really make sense in this context. See for example the discussion of the so-called Einstein-Rosen bridge (wormhole of a kind) in the discussion of nonrotating black holes modeled by the Schwarzschild vacuum solution in MTW, Gravitation; see General relativity resources for full citation. On the other hand, you could ask for the area of the event horizon. This has no immediate physical meaning but it is mathematically well defined and has a profound meaning in terms of the global structure of a black hole spacetime. Then the brief answer to your question is that it can be computed in terms of the parameters mentioned in the no hair theorem. See for example Frolov & Novikov, Black Hole Physics (full citation given in the article just mentioned). ---CH 03:16, 2 February 2006 (UTC)

John Wheeler

I believe I read in one of Kip Thorne's books that John Wheeler coined the term: "Black holes have no hair." Is this correct? David618 02:52, 12 March 2006 (UTC)

Yes. The book was no doubt Black Holes And Time Warps : Einstein's Outrageous Legacy, a popular book which contains many anecdotes about the Golden age of general relativity. ---CH 16:45, 14 March 2006 (UTC)

I thought it was from that book. Thanks. David618 15:39, 15 March 2006 (UTC)

The article used to source the name from JAW. For some reason this has been lost. Why? --Michael C. Price ^talk 17:01, 19 February 2009 (UTC)

"Black holes have no hair." <-- What does this mean, exactly? Is 'hair' something like information?

yes. --Michael C. Price ^talk 17:01, 19 February 2009 (UTC)

Students beware

I edited earlier versions of this article and had been monitoring it for bad edits, but I am leaving the WP and am now abandoning this article to its fate. And WikiProject GTR is presumably defunct.

Just wanted to provide notice that I am only responsible (in part) for the last version I edited; see User:Hillman/Archive. I emphatically do not vouch for anything you might see in more recent versions, although I hope for the best.

Good luck in your search for information, regardless!---CH 02:28, 1 July 2006 (UTC)

Conserved quantities

Mustn't all conserved quantities be conserved in a black hole as well? Granted most particle quantum numbers are violated in one process or another, but what about exact laws like conservation of color charge, or B−L? 164.55.254.106 19:55, 18 July 2006 (UTC)

The no hair theorem deals only with classical gravitational and electromagnetic fields, under classical general relativity. If you were to add in new additional classical fields, it seems to me entirely likely that you would get new additional conserved quantities (but I'll leave it to the real GR experts here to pronounce definitively).

Note also that the quantum case is an entirely different ball game. If black holes have an entropy S, that implies that there are exp(S/k) conceptually identifiable different quantum states asscociated with each classical state. Jheald 21:27, 18 July 2006 (UTC).

What about Momentum (non angular)?

I don't understand why this theorem explicitly states that black holes retain mass and angular momentum but says nothing about normal, linear momentum. I suppose it's considered obvious to an expert in the field? I can't imagine that a rapidly moving star ceases to move when it collapses in to a black hole (as if there were some coordinates throughout the universe such that non movement could even be defined). If I wanted to characterize a black hole COMPLETELY, I would need one number for mass, one signed number for charge, one 2 vector for direction of movement and a scalar for magnitude of movement, and one two vector for axis of rotation and a scalar for speed of rotation. Is that correct?

Momentum isn't considered a property of the black hole as it depends on reference frame. We only consider the frame-independent magnitude of the momentum, which is the mass. (Similarly, we only consider the magnitude of the angular momentum as a property, but not the direction) Ben Standeven 23:34, 29 November 2006 (UTC)

Possible Reference to be included

I am not an expert in the field, but one might include "Black Hole Uniqueness Theorems" by Markus Heusler, Peter Goddard (editor) and Julia Yeomans (editor) because it gives an overview about the subject (without quantum gravity).

Cosmological constant

http://arxiv.org/abs/gr-qc/0702006 "No hair theorems for positive $\Lambda$" which starts off:

"We extend all known black hole no-hair theorems to space-times endowed with a positive cosmological constant $\Lambda.$ "

seems to extend the non-hair theorem for black holes to universes which have a cosmological constant.--Michael C. Price ^talk 02:11, 1 July 2007 (UTC)

http://arxiv.org/abs/gr-qc/9606008 "Eluding the No-Hair Conjecture for Black Holesstates"

I discuss a recent analytic proof of bypassing the no-hair conjecture for two interesting (and quite generic) cases of four-dimensional black holes: (i) black holes in Einstein-Yang-Mills-Higgs (EYMH) systems and (ii) black holes in higher-curvature (Gauss-Bonnet (GB) type) string-inspired gravity. Both systems are known to possess black-hole solutions with non-trivial scalar hair outside the horizon. The `spirit' of the no-hair conjecture, however, seems to be maintained either because the black holes are unstable (EYMH), or because the hair is of secondary type (GB), i.e. it does not lead to new conserved quantum numbers.

which also seems relevant. --Michael C. Price ^talk 02:19, 1 July 2007 (UTC)

Hairy balls

Is this "black holes have no hair" statement related to the "hairy ball" observation? A "hairy ball" (e.g. the physiscist's standard spherical vacuum-racing hamster) cannot have all of the hair smoothed down perfectly flat. In at least two points ("boojums" if you'd like more physics-related neologisms) the hair must either come to either a radial point, or a point of extreme curl. As such points aren't observable from outside the event horizon, we can infer that there's no "hair" on a black hole, where this "hair" analogy can be extended to a number of forms of possible "texture" in its surface. Andy Dingley (talk) 11:15, 15 April 2008 (UTC)

No. This conjecture is about a very different type of 'hair'. 130.237.201.40 (talk) 14:12, 21 October 2008 (UTC)

Hmmm, "a very different type of 'hair'"? Is there no similarity between combing & frame-dragging? Does a 2-sphere black hole not have 2 frame-dragging "dead" spots whereas a 2-torus frame-drags everywhere? 86.135.127.147 (talk) 04:25, 10 October 2010 (UTC)

Classical/Quantum Entropy

Is the final word supposed to be 'isentropy' and not 'isotropy'? I thought we were talking about entropy, and not space... 128.171.31.11 (talk) 02:27, 30 April 2008 (UTC)

Hypotheses

Surely a hypothesis that the black hole is stationary should be included in the first sentence. I think a hypothesis that the space-time is real analytic is also necessary. 130.237.201.40 (talk) 14:30, 21 October 2008 (UTC)

Is it proven?

Misner, Thorne, & Wheeler (1973) says that although a series of theorems by Hawking, Carter, and Israel "come close" to proving it, it was not technically proven. Ludvigson (1999) says it's proven except for "details". Hall, Pulham (1996) regard it as proven and give an outline. Chow (2008) says it was proved by Carter, Hawking, Israel, Robinson, and Price. So I guess the article should say it's "regarded as proven"? --Chetvorno^TALK 08:10, 28 March 2010 (UTC)

In the book Recent Advances in General Relativity: Essays in Honour of Ted Newman (1992), Israel writes:

"The 'no hair' conjecture has over the years almost come to assume the status of an uncritically accepted paradigm. The spate of recent work in this area (e.g., Krauss and Wilczek 1989) has been salutary in exposing the severe limitations of such a paradigm. Of particular interest is the very recent discovery by Campbell, Duncan, Kaloper, and Olive (1990) that rotating black holes can support stable axionic hair."

This source is twenty years old and I don't know if the status has changed. If it hasn't been properly proven, then it would be wrong to label this as a 'theorem'. Does anyone have up-to-date information on this matter? --JB Gnome (talk) 04:27, 20 January 2012 (UTC)