Talk:No-hair theorem

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 Ball Observation
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)


 * sorry for reviving this old discussion, but given that this is not the first mention of this apparent similarity, i thought i'd revive the discussion. what do you guys think about the issue? couldn't we relate the "hair" (information) about the matter that created, and is absorbed by, the event horizon of the black hole to the properties of the tangent space (i.e. derivative)? sorta spitballing obv, but it sure seems i'm not the only one who sees a potential relationship that may be worthy of further discussion.174.3.155.181 (talk) 17:55, 2 July 2016 (UTC)
 * I don't understand what you're talking about. Please elaborate. I'm also going to remove the RfC template, since there's no RfC question (or if there is, it's not easily understood). Banedon (talk) 01:58, 19 July 2016 (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)


 * Perhaps someone who (unlike me) actually understands this stuff could add a section on progress toward a proof; the contributory theorems which have actually been proved so far. -- Chetvorno TALK 23:31, 13 August 2012 (UTC)


 * "The no-hair theorem, proved by the combined work of Israel, Carter, Robinson and myself, shows that the only stationary black holes in the absence of matter fields are the Kerr solutions...characterized by two parameters, mass M and angular momentum J. The no-hair theorem was extended by Robinson to the case where there is an electromagnetic field. The no-hair theorem has not been proved for the Yang-Mills field, but the only difference seems to be the addition of one or more integers that label a discrete family of unstable solutions. It can be shown that there are no more continuous degrees of freedom of time-independent Einstein-Yang-Mills black holes" -Hawking & Penrose, 2010, p.39
 * -- Chetvorno TALK 23:57, 13 August 2012 (UTC)

"Black holes in quantum gravity" section
This is a long, uncited section, and it seems to me that it is mostly unrelated to the article topic. --192.75.48.150 (talk) 15:51, 3 April 2013 (UTC)


 * It appears to be a theoretical argument that the no-hair theorem is not strictly true at a quantum level, but is merely a classical approximation. As such, it is relevant to the article. But it would be nice to have a reference for it. JRSpriggs (talk) 08:11, 4 April 2013 (UTC)

Clarification of Example
The Example currently mentions two black holes with identical properties, except that one is made of ordinary matter, while the other is made of anti-matter. The example states that to an outside observer, the two holes are indistinguishable. Fine. If two such black holes were to collide, I imagine that the result would be different from a collision involving two black holes made of the same type of matter. In other words in the event of a collision, it would become clear if the two holes were or were not made of the same type of matter. Would it be possible to expand the explanation to briefly include the case of a collision of the two mentioned black holes ? Lklundin (talk) 08:27, 6 April 2013 (UTC)


 * The following is, of course, speculation: Actually there is no difference between a black hole formed from ordinary matter and one formed from anti-matter. A collision between them would be exactly the same as a collision between two black holes formed from ordinary matter (or two formed from anti-matter, or two formed from dark matter). Once the contents have been crushed to a singularity at the center, their origin is no longer relevant to whatever they have become. JRSpriggs (talk) 13:00, 6 April 2013 (UTC)
 * Thanks, that sounds consistent with the information in the article. In my (limited) understanding, if matter and anti-matter in a normal state were to collide, the mass would cease to exist and instead be converted to energy. If I understand the Example and the above explanation correctly, this would not be the case for a collision of black holes that originated from matter and anti-matter. Rather if I understand things correctly, such a collision would form a new black hole, with a mass equal to the sum of the two collided black holes. I think a short, specific explanation of this would help to make it clear that the type of matter (matter or anti-matter) that formed the black hole is lost in the collapse. Lklundin (talk) 13:22, 6 April 2013 (UTC)
 * if two BH with equal mass M but opposite electric charge Q and -Q, then in Reissner–Nordström metric the sign of

r_{Q}^{2} = \frac{Q^2 G}{4\pi\varepsilon_{0} c^4}. $$
 * would not change and they have the same RN metric, right ?. In the Lklundin's case, two BH has Q = 0? Earthandmoon (talk) 14:49, 6 April 2013 (UTC)


 * It is generally believed that black holes will not have any significant electric charge, i.e. $$r_Q \ll r_S \,.$$ This is because a charged celestial body would repel like charges and attract unlike charges until it has been effectively neutralized.
 * Two colliding black holes should emit a burst of gravitational radiation as they spiral inward towards their common center of mass, and then coalesce into one black hole.
 * Mass and energy are quantitative attributes of matter and radiation; they are not things which exist in themselves and inter-convert. Indeed, energy is conserved, i.e. it cannot be created nor destroyed, merely transferred between different things. JRSpriggs (talk) 21:27, 6 April 2013 (UTC)

Magnetic dipole moment?
Is there any intuitive way of understanding why a magnetic moment is not possible? Given tthat a charge is possible, and that angular momentum is possible, plain-old gut sense suggests that a magnetic dipole moment should be possible. I can think of hand-waving arguments to banish higher-order magnetic moments, but not the dipole. But surely, there is a way to do this? 67.198.37.16 (talk) 21:56, 30 July 2015 (UTC)
 * Magnetic dipole moment in fact equals (charge / mass) × (angular momentum), see equation (33.10) on p. 892 in Misner, Thorne, Wheeler "Gravitation" (ISBN 978-0716703341), so it must be non-zero for electrically charged rotating black holes. — Mikhail Ryazanov (talk) 18:20, 23 July 2022 (UTC)

Recent publication - soft hair
There's a new publication about "soft hair" on black holes retaining some of the information:. Could someone with more knowledge of the subject than me please edit that in? 2A02:810D:14C0:5A0C:20B7:15AE:50A5:C945 (talk) 21:06, 8 June 2016 (UTC)


 * The article already mentions "excepting quantum fluctuations". JRSpriggs (talk) 01:16, 9 June 2016 (UTC)

Limitations
I guess, the "theorem" conditions should state that it is limited to isolated black holes in equilibrium. Because, for example, when two black holes merge to form a single black hole, this non-stationary solution has more degrees of freedom than just the total mass, charge and angular momentum (see ). Or when something falls into a black hole, it also breaks the BH symmetry and creates "ripples" on its event horizon (leading to radiation of gravitational waves as the BH equilibrates). — Mikhail Ryazanov (talk) 05:00, 12 January 2020 (UTC)

How or Why?
The article explains the "results" of the theorem, ie what the theorem states, what the implications are. But what is the rationale behind the conjecture? How was it derived? For example "why" wouldn't it make a difference if the black hole was composed of matter or antimatter?Feldercarb (talk) 01:04, 15 July 2022 (UTC)

Some black holes may yet have hair. (lol)
If the black hole no longer has sufficient feed and radiates outward more energy than absorbed, it shrinks. This means that the event horizon is also shrinking, which in turn means that some information AKA 'hair' may yet be observed, if and when that information is stuck within the outer edge of the event horizon. This may constitute 'hair' and therefore shrinking black holes may yet not be (entirely) baldies.

More seriously, if we can find a black hole that is shrinking 'fast' and is nearing the minimum size of a black hole, then we may yet also experience/observe what the black hole is made of once it decompresses completely. At least we'd see how far a black hole can shrink before undergoing such decompression.