Talk:Black hole thermodynamics

Introduction
(William M. Connolley 17:31, 2004 May 26 (UTC)) Errrm... is this page dodgy? It starts off by saying that inside BH's classical thermo breaks down. Then it derives a pile of things using classical thermo. Then electrons go back in time.


 * I have no recollection of editing the intro; but I clearly did about six months ago. So you may rightly be suspicious of that bit. Charles Matthews 18:32, 26 May 2004 (UTC)

Request for review
Requesting someone who is experienced in astrophysics looks over this article, becuase it's quite confusing and I'm not sure if it's all correct (September 2006) —The preceding unsigned comment was added by 86.133.225.32 (talk • contribs) on 23:02, 31 August 2006.


 * To whoever is willing to improve the article, here is a link to a review article: Don N. Page, Hawking radiation and black hole thermodynamics, New Journal of Physics 7 (2005) 203.. --Lambiam Talk  18:16, 29 October 2006 (UTC)


 * Thanks (although the link seems to be broken), I plan on improving this article sometime, only I can't say when. I have a copy of Wald's 1994 Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, which I will use to clean this article (although I still like to find one more book).  Later: --Sadi Carnot 19:38, 1 November 2006 (UTC)


 * Sadi, I recommend the book by Birrel and Davies: Quantum Field Theory in Curved Space. -Joshua Davis 23:01, 13 January 2007 (UTC)

Some sample calculations would be helpful, as the proper units to use are not obviouus to persons trained in other fields. ie mass in kilograms, distance in meters, gravity in meters per sec, per second k =? 12:02, 5 September 2007 (UTC) —Preceding unsigned comment added by Ccpoodle (talk • contribs)

Proportionality
Shouldn't we say that the constant of proportionality is approximately 1/4, up to quantum gravity corrections, or is it somehow proven to be 1/4 regardless of what gravity looks like at Planck scale? Itinerant1 03:00, 12 January 2007 (UTC)--


 * There have indeed been cases studied where quantum corrections change it from 1/4. But this may be too technical to get into here.  PhysPhD 06:42, 19 May 2007 (UTC)

Deleted "Problems" sections
There may be some parts of these sections that could be salvaged, but they were way below the bar as they stood. All that stuff with waves and rolling dice was some author making stuff up.PhysPhD 06:42, 19 May 2007 (UTC) It was all quoted from Hawking sciam (not physical review) article, so i dont know ho you might consider it making stuff up, the work about the duality of time arrows comes from Santa Fe institute work done by gellmann and George west (nobel prize and ex-president of alamos lab), so it is not original research, the general view of relativity comes from Gravitation by Wheeler, i will repost latter a shorter version. I acknoledge english is not my first language, but also a need in this encyclopedia of better defined concepts - most people dont undestand its mathematics, and critical opinions (which is idfferent fro oroginal research). That is what the britannica and larousse have and wikipedia lacks because most students who work here tend to have limited knowledge to do those improvements, which however distinguish a truly good encyclopedia like those 2 - —Preceding unsigned comment added by 76.89.242.7 (talk) 01:10, 23 February 2008 (UTC)

Black hole Evaporation?
The "laws of black hole mechanics" section lists dA > 0 as one of the laws, i.e. that black holes never decrease in size. Hasn't this theory been supplanted by the theory of black hole evaporation which allows black holes to shrink, and is in fact part of black hole thermodynamics? —Preceding unsigned comment added by 24.6.210.135 (talk) 07:51, 29 March 2009 (UTC)


 * Yes, that is correct. This law was disproved by Hawking.  I guess the correct law is just dS/dt > 0, where the term $$kA/4l_P$$ is included in the expression for S.  I will update the article with a note that this law has been superseded, but it would be good if someone with more knowledge of the subject and its history would take a closer look at this article and make it clearer.


 * (btw, pet hate: it should read dA/dt > 0, not just dA > 0, as the latter would imply that both dA/dt > 0 and dA/d(-t) = -dA/dt > 0, which is impossible) Nathaniel Virgo (talk) 14:36, 11 April 2010 (UTC)

Then dA/dt < 0 implies d(S_BH)/dt < 0 for BH evaporation, assumed to be a dissipative process. dA/dt < 0 either violates the second law or we assume that evaporation is not an irreversible process!

Poor Quality

 * I am a chemist and fixed the parts on the page pertaining to thermodynamics. A lot of the definitions were sub par and the one for the 3rd law was flat out wrong. Whoever wrote this clearly has no training or grasp of thermodynamics. I do not know the quality of the astrophysics part, but from looking at it and reading other comments, this page is an unfortunate exception to wiki's very accurate scientific articles. Alchemist314 (talk) 09:34, 13 November 2010 (UTC)

As currently written, the part about the 3rd law is quite confusing, as it suddenly jumps from black hole thermodynamics to crystalline substances (which have nothing to do with black holes). ~ Peterwshor (talk) —Preceding undated comment added 13:13, 12 March 2011 (UTC).

Simply Wrong
You don't need an astrophysicist to look at the article. It is completely wrong. If the entropy is proportional to the area then you don't need temperature. It exists at absolute zero, and the third law? The point that the area increases while evaporation decreases the area is well-taken. Evaporation by black-body radiation is complete nonsense. You need a thermal source to keep the walls of the cavity at a given temperature so that the radiation will be thermal at that temperature. If the black hole is the final state what would give rise to a finite temperature that would allow for thermal radiation? The zeroth law is also wrong. It say that when two bodies at different temperatures are placed in thermal contact they will arrive at thermal equilibrium at a common temperature. What does it mean for a black hole to have a uniform temperature? Is it possible for a gradient in temperature to exist? Temperature inversely proportional to the energy (mass) is also wrong. The entropy must be a concave function, i.e. a negative second derivative, not a convex function. Concave functions are to be maximized, convex functions minimized. The Bekenstein-Hawking expression is a convex function of the mass (energy), and, hence, it is not a candidate for an entropy at all. See arXiv:1110.5322v1 and http://www.youtube.com/watch?v=dpzbDfqcZSw for more detailed criticisms.Bernhlav (talk) 04:45, 26 December 2011 (UTC)bernhlav.

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Blank entire section on quantum corrections
I am blanking the following content, reproduced below. Its a mass of equations arriving without explanation, background, introduction, and far beyond the level of even sophisticated readers. Copying it here, because the shear heft is awesome. I am also removing nearly identical text that was added to Hawking radiation, Quantum gravity and Reissner–Nordström metric. If I recall correctly, there was also a fifth article, I think I blanked that one half a year ago. It appears to be associated with self-promotional placement that was added shortly after the last citation appeared in print. I'm directing those other talk pages to this one.


 * Quantum gravitational corrections to the entropy
 * The Hawking formula for the entropy receives corrections as soon as quantum effects are taken into account. Any UV finite theory of quantum gravity should reduce at low energy to General Relativity. Works pioneered by Barvinsky and Vilkovisky   suggest as a starting point up to second order in curvature the following action, consisting of local and non-local terms::$$\begin{align}\Gamma=&\int d^4x\, \sqrt{-g}\,\bigg(\frac{R}{16\pi G}+c_1(\mu)R^2+c_2(\mu)R_{\mu\nu}R^{\mu\nu}    +c_3(\mu)R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\bigg)\\    -&\int d^4 x \sqrt{-g}\bigg[\alpha R\ln\left(\frac{\Box}{\mu^2}\right)R    +\beta R_{\mu\nu}\ln\left(\frac{\Box}{\mu^2}\right)R^{\mu\nu} + \gamma R_{\mu\nu\rho\sigma}    \ln\left(\frac{\Box}{\mu^2}\right)R^{\mu\nu\rho\sigma}\bigg],\end{align}$$where $$\mu$$ is an energy scale. The exact values of the coefficients $$c_1,c_2,c_3 $$ are unknown, as they depend on the nature of the ultra-violet theory of quantum gravity. $$ \ln\left(\Box/\mu^2\right)$$  is an operator with the integral representation:$$    \ln\left(\frac{\Box}{\mu^2}\right)=\int_0^{+\infty}ds\, \left(\frac{1}{\mu^2+s}-\frac{1}{\Box+s}\right).$$The new additional terms in the action modify the classical Einstein equations of motion. This implies that a given classical metric receives quantum corrections, which in turn shift the classical position of the event horizon. When computing the Wald entropy, one then takes the shifted position $$r_h$$ of the event horizon into account::$$     S_{\text{Wald}}=-2\pi \int\limits_{r=r_h} d\Sigma\, \epsilon_{\mu\nu}\epsilon_{\rho\sigma}\frac{\partial \mathcal{L}}{\partial R_{\mu\nu\rho\sigma}}.$$Here, $$\mathcal{L}$$ is the Lagrangian density of the theory, $$d\Sigma=r^2\sin\theta d\theta d\phi$$, $$R_{\mu\nu\rho\sigma}$$ is the Riemann tensor and $$\epsilon_{\mu\nu}$$ is an antisymmetric tensor normalised as $$\epsilon_{\mu\nu}\epsilon^{\mu\nu}=-2.$$This method was applied in 2021 by Calmet et al. for Schwarzschild black holes. The Schwarzschild metric does not receive quantum corrections at second order in curvature and the entropy is:$$    S_{\text{Schw}}=\frac{A}{4G}+64\pi^2c_3+64\pi^2\gamma\Big[\ln\left(4G^2M^2\mu^2\right)+2\gamma_E-2\Big].$$A generalisation for charged (Reissner-Nordström) black holes was subsequently carried out by Campos Delgado. 

67.198.37.16 (talk) 02:49, 22 May 2024 (UTC)


 * First thing to note, generally we don't copy-paste sections of articles onto talk pages, as this makes them unreadable. If you want to reference a specific edit or section, I suggest you link it by copying the diff, like this. Secondly, this is a technical article about some pretty high-level physics, so one would expect complex equations like those you removed. I'm not sure what you mean when you say that the section lacks context, as there is quite a bit of context surrounding the equations. I suggest you check out Jargon for more information on technical language on Wikipedia. For these reasons, I have reverted your edits. If you would like to edit the article to include a lower-level explanation of this section, you can, but removing a large amount of well-sourced content doesn't seem like a good idea. Catalyzzt (talk) 03:09, 22 May 2024 (UTC)
 * Umm, I actually understand what those equations are saying. They are utterly inappropriate for this article. They are self-promotional spam, presumably from the last cited author. There is a small ocean of far more important stuff that can be said in this article, before the above is addressed. 67.198.37.16 (talk) 03:15, 22 May 2024 (UTC)
 * Wikipedia relies on reliable sources for information. The sources provided were published in reputable journals. Please provide a reliable source disputing this content, otherwise it looks a lot like WP:OR. Adam Black  t &bull;  c 03:29, 22 May 2024 (UTC)
 * See above. While unsourced material may be challenged without any explanation, sourced material requires more than just saying "this source is bad". Catalyzzt (talk) 03:43, 22 May 2024 (UTC)
 * There are multiple issues here. A mundane one is that these are primary sources, not secondary. Another issue is that almost exactly the same content was added to four different articles. A third issue is that the content is not particularly notable. There are more important and interesting topics that these four articles do not cover, but should. If it was actually notable, then it could be covered in a single article, (not cut-n-pasted into four of them). Doing this would require all the conventional rules of WP article structure: what's it about, an informal introduction, a review of the competing theories of quantum gravity, and which one this was derived from. Then a review of the classical action, then a review of what terms are possible in a quantum action. A discussion of gauge invarience. Then a review of contributing loop diagrams. Were there special vierbeins that were used to obtain this? A guage fixnig term, perhaps?. Why only scalar, Ricci and Riemann curvature terms, why not torson or contorsion terms?  And what about that renormalization term with mu in it? Is it anonomalous? Ordinary?  Many of these kinds of theories have solitions or instantons in them. Does this one? Are there string terms? Was this obtained by supersymmetric arguments?  There's an old joke: there are more theories of quantum gravity than there are researchers studying it. This is certainly an interesting topic, and perhaps an article could be devoted to it. But four cut-n-paste copies of dense jargon that are opaque even to experts in the field isn't appropriate. 67.198.37.16 (talk) 03:57, 22 May 2024 (UTC)
 * I have also removed some other Campos Delgado spam, so I think you're right about this being self-promotion (EDIT: I confirmed that it was added by the same user that added citations to Campos Delgado everywhere, and went on a spree removing them from Primary field, Liouville field theory, Black hole, and Hawking radiation).
 * Independently of that, I concur that this content is WP:UNDUE. Even taken a face value it is just one possible second-order correction. It would be worth reporting if it were a well-stablished theory (as supported by secondary sources). Even then it would belong in a single article, copy-pasting the same content everywhere is indefensible. Tercer (talk) 07:39, 22 May 2024 (UTC)
 * I notice my reversion of your blanking on Hawking radiation has been reverted. I am not going to revert again for risk of getting into an edit war. You appear to be a very experienced editor, so please take your own advice in the edit summary on joining the discussion. Wait for consensus before removing referenced content. You were bold and removed content, I contested that bold action by reverting it, you should then be waiting for the discussion to conclude before restoring your bold action. My background is in mathematics (I have a bachelors degree in mathematics and I'm currently studying for my masters); I've studied a decent amount of physics but this specific subject matter is beyond my expertise. My reversion was based on Wikipedia policy, not out of a certainty that it should be included or as an endorsement of the contents accuracy. I am leaving it to more qualified editors to discuss here and come to a consensus about whether the material should remain. Also as I said above, your actions did come across as WP:OR. Adam Black  t &bull;  c 17:18, 22 May 2024 (UTC)
 * I don't think we should lump the Delgado and Barvinsky/ Vilkovisky works.
 * The Delgado paper is very new (WP:TOOSOON) and not highly cited. It should just be removed.
 * The Barvinsky work should not have 4 primary citations. Several of these papers are highly cited and therefore the content should be based on secondary, review articles. However, a recent review with over 600 citations does not mention Barvinsky (or Delgado) but does discuss quantum gravity.
 * Almheiri, A., Hartman, T., Maldacena, J., Shaghoulian, E., & Tajdini, A. (2021). The entropy of Hawking radiation. Reviews of Modern Physics, 93(3), 035002.a
 * Johnjbarton (talk) 17:39, 22 May 2024 (UTC)
 * Maldacena is a highly respected author, and presumably the RMP article is well-written, clear, informative, educational (As a reminder: RMP, "Reviews of Modern Physics", mostly publishes actual reviews, something that starts at "square one" and gets you up to speed on that particular topic. So 600 citations is hardly surprising for something well-written.) If someone were to read that review, and claim to understand it, and boil it down to one or three or 5 or 10 paragraphs that could be added to this article, that would be ... excellent!
 * I am also 99.999% certain (five-sigma) that the quantum action up above appears nowhere in the Maldacena review. All right, maybe just four sigma. All right, three sigma, I do make mistakes at a human-mistake-making-frequency-level. I still hold that in the context of the present article, the eqns above are far too dense, just a blob of opaque jargon plopped into the middle of what is a non-technical, for-the-science-enthusiast article. If the Barvinsky/ Vilkovisky work is noteworthy, then let's make an actual article, that actually explains what all that stuff means, We have plenty of articles on WP that could be wikilinked to explain actions and tensors and loop diagrams, and so a good article could be written, if someone took the effort. The current form, above, though, is unacceptable. 67.198.37.16 (talk) 07:48, 23 May 2024 (UTC)
 * To illustrate the point: how many people in this conversation know what $$\sqrt{-g}$$ is called, why there's a minus sign in there, and how to actually obtain a value for it? I know what it is, and if you also know, don't spoil it (Hint: alternative notation for the same thing is $$*\omega$$). Yes, WP has one maybe three articles explaining what it is. Now imagine being the science enthusiast interested in knowing more about BH thermo, and you see this eqn, what exactly do you learn? That formulas are complicated? Next, imagine being an expert, able to not only recognize each and every symbol used in those formulas, but have actually computed their values in a variety of contexts. What do you get out of it? Personally, I've computed plenty of curvature tensors and loop diagrams in my life, and I look at that formula, and kind of get nothing out of it, other than warm fuzzies that it looks plausible, conventional, and not totally alien. I don't think WP is in the industry of creating warm fuzzies. 67.198.37.16 (talk) 08:08, 23 May 2024 (UTC)


 * I don't believe that this section is overly complicated or technical for inclusion, on the contrary for articles on mathematics equations usually are incredibly useful. Essentially every single math article does this take say the Pythagorean theorem or any article relating to geometry. I don't think that simply because the equations become more difficult to understand it should be removed. To me it doesn't make sense, the equations are directly related to the content, while yes the equations are more difficult to understand then say simple geometry it is the same principle, not including equations results in large amounts of information being lost. From experience equations as a reference are always incredibly useful to the reader. Des Vallee (talk) 17:35, 4 June 2024 (UTC)
 * I don't think that simply because the equations become more difficult to understand it should be removed.
 * I agree. But the content proposed is not notable, and certainly not 4 copies of it. Johnjbarton (talk) 18:31, 4 June 2024 (UTC)