# What's Wrong With Black Hole Thermodynamics?

by juanrga
Tags: black hole, thermodynamics
 P: 476 An interesting review of usual claims done in black hole literature by an expert in thermodynamics.
PF Gold
P: 4,775
 Quote by juanrga An interesting review of usual claims done in black hole literature by an expert in thermodynamics.
Can you reference the abstract rather than the PDF.

I've seen some other critical reviews of this. If I can find them, and they are in similar spirit, I'll post them here.

[EDIT: Here is the abstract link: http://arxiv.org/abs/1110.5322
 Emeritus Sci Advisor P: 7,361 http://adsabs.harvard.edu/abs/1980PhLA...78..219L "Entropies need not to be concave" seems to be in some disagreement about one of the major premises of the author. I stumbled over this while trying to see if the original paper was peer reviewed - I see other peer reviewed papers by the author, but I haven't found that the arxiv paper was ever published. Unfortunately the published papers mostly seem to require subscriptions to access.
P: 5,630

## What's Wrong With Black Hole Thermodynamics?

yea, well Hawking thought Beckenstein was wrong as well....until Hawking arrived at Beckenstein's answer using a completely different approach.

Besides:
 Although Hawking's calculations gave further thermodynamic evidence for black hole entropy, until 1995 no one was able to make a controlled calculation of black hole entropy based on statistical mechanics, which associates entropy with a large number of microstates. In fact, so called "no hair"[7] theorems appeared to suggest that black holes could have only a single microstate. The situation changed in 1995 when Andrew Strominger and Cumrun Vafa calculated the right Bekenstein-Hawking entropy of a supersymmetric black hole in string theory, using methods based on D-branes. Their calculation was followed by many similar computations of entropy of large classes of other extremal and near-extremal black holes, and the result always agreed with the Bekenstein-Hawking formula.
http://en.wikipedia.org/wiki/Black_hole_thermodynamics

It would be fun, though, if the cited paper above added new insights.....Anything there??
PF Gold
P: 4,775
 Quote by pervect http://adsabs.harvard.edu/abs/1980PhLA...78..219L "Entropies need not to be concave" seems to be in some disagreement about one of the major premises of the author. I stumbled over this while trying to see if the original paper was peer reviewed - I see other peer reviewed papers by the author, but I haven't found that the arxiv paper was ever published. Unfortunately the published papers mostly seem to require subscriptions to access.
I also noticed that only a few of the early paper by this author were peer reviewed, but not this one. "Expert on Thermodynamics" seems a little overblown relative to the published history. But I didn't want to bring this up until I had tried to digest the paper for its content.
P: 476
 Quote by pervect http://adsabs.harvard.edu/abs/1980PhLA...78..219L "Entropies need not to be concave" seems to be in some disagreement about one of the major premises of the author. I stumbled over this while trying to see if the original paper was peer reviewed - I see other peer reviewed papers by the author, but I haven't found that the arxiv paper was ever published. Unfortunately the published papers mostly seem to require subscriptions to access.
The word «entropy» is used with different meanings by many people; very often those meanings are not compatible with the well-established concept of thermodynamic entropy.
P: 476
 Quote by PAllen I also noticed that only a few of the early paper by this author were peer reviewed, but not this one. "Expert on Thermodynamics" seems a little overblown relative to the published history. But I didn't want to bring this up until I had tried to digest the paper for its content.
Curious, instead reviewing the work cited, people here goes on reviewing the author.

Well, he is a well-known expert in thermodynamics, their works are cited by other thermodynamicians and his book in thermodynamics of irreversible processes is published by Dover classics.

He has received Galilei Gold Medal 2009
 For his work on irreversible thermodynamics and contributions to many areas of physics including that of Brownian motion, and in the establishment of the statistical basis of thermodynamics, and his contributions in astrophysics/cosmology.
And with a simple search in google scholar I can find

The thermodynamics of endoreversible engines
BH Lavenda - American Journal of Physics, 2007 - link.aip.org

Mean entropies
BH Lavenda - Open Systems & Information Dynamics, 2005 - Springer

High temperature properties of the MIT bag model
BH Lavenda - Journal of Physics G: Nuclear and Particle …, 2007 - iopscience.iop.org

...

It is difficult to believe that are not peer reviewed...
 P: 6,863 The paper seems to be gooble-gook. C_p is a derivative and can be be negative or non-existent. He does a lot of equations based on the behavior of classical ideal monatomic gases, which I suppose merely shows that black holes are not made of classical ideal monatomic gasses.
P: 6,863
 Quote by juanrga Well, he is a well-known expert in thermodynamics, their works are cited by other thermodynamicians and his book in thermodynamics of irreversible processes is published by Dover classics.
And I've known extremely brilliant people in one field that were cranks when they were in another one. Roger Penrose is an example. One thing about the author is that he seems to have no experience dealing with objects in which the gravity field makes a considerable contribution to the system, which is not good when you are dealing with black holes. He seems to miss completely the point about polytropes.

He might be brilliant in thermodynamics in other fields, but the arguments that he is giving in that paper seems to be total non-sense.

I may not be an "expert in thermodynamics" but I do know a thing or two about collapsed systems. His arguments make absolutely no sense because in any sort of stellar object, you are moving energy back and forth between the material object and the gravity field, and you can't just take an object and consider only the themodynamic energy. If you want to do your bookkeepping right, you have to consider the energy that is in the gravity field, which he doesn't do.

Since he isn't including the energy in the gravity field, all of his other arguments fall apart. If you include gravity, you get the results in the first section, which he doesn't seem to understand.
 Sci Advisor PF Gold P: 1,767 I note in the paper he also invokes a strong form of the 3rd law, $\lim_{T\to 0}S = 0$. This form ignores residual entropy due to a degenerate ground state. He is here ignoring degeneracy. His reasoning may be implicitly the "no hair" theorem but that doesn't apply. The very debate, whether BH's evaporate, is a question of observing "internal" degrees of freedom in the configurations of emitted thermal radiation (here "internal" to the surface configuration?). Reading the short paper, he is invoking analogue physical systems (partitioned volumes, ideal gasses) without any direct thought experiments about a BH per se. I don't see the paper pointing out any physical contradictions, only the exceptional behavior of BH thermodynamics.
P: 476
 Quote by twofish-quant The paper seems to be gooble-gook. C_p is a derivative and can be be negative or non-existent. He does a lot of equations based on the behavior of classical ideal monatomic gases, which I suppose merely shows that black holes are not made of classical ideal monatomic gasses.
C_p is not a mere derivative, but a physical quantity with determined properties. Your 'argument' could be re-used to say that (4) "is a derivative and can be be negative or non-existent", but it is difficult to believe someone would accept negative or non-existent mass for a black hole or an imaginary speed of light or similar nonsense...

Effectively, nowhere he says or even suggests that black holes are made of "classical ideal mono-atomic gasses". He uses the simple case of an ideal gas for illustrating the difference between c and C.
P: 476
 Quote by twofish-quant And I've known extremely brilliant people in one field that were cranks when they were in another one. Roger Penrose is an example. One thing about the author is that he seems to have no experience dealing with objects in which the gravity field makes a considerable contribution to the system, which is not good when you are dealing with black holes. He seems to miss completely the point about polytropes. He might be brilliant in thermodynamics in other fields, but the arguments that he is giving in that paper seems to be total non-sense. I may not be an "expert in thermodynamics" but I do know a thing or two about collapsed systems. His arguments make absolutely no sense because in any sort of stellar object, you are moving energy back and forth between the material object and the gravity field, and you can't just take an object and consider only the themodynamic energy. If you want to do your bookkeepping right, you have to consider the energy that is in the gravity field, which he doesn't do. Since he isn't including the energy in the gravity field, all of his other arguments fall apart. If you include gravity, you get the results in the first section, which he doesn't seem to understand.
It is evident that this kind or argument can be inverted. People as Hawking, experienced in black holes and general relativity, can say nonsense when entering in the field of thermodynamics.

Even if we ignore now that «the energy that is in the gravity field» is not well-defined in general relativity, what you say about thermodynamic energy and gravitation seems to be without any basis.

Already many ordinary textbooks explain how gravitational energy $M\phi$ contributes to thermodynamic energy. Of course, in a BH the situation is more complex and $M\phi$ is not enough, but thermodynamics in presence of gravitation continues to hold and I fail to see your point.
P: 6,863
 Quote by juanrga C_p is not a mere derivative, but a physical quantity with determined properties. Your 'argument' could be re-used to say that (4) "is a derivative and can be be negative or non-existent", but it is difficult to believe someone would accept negative mass for a black hole or imaginary speed of light or nonsense as that...
In the context of black holes and stars, it isn't. You add energy, the gravitational field rearranges itself and you get a different temperature. C is a quantity that includes both the effects of gravity and the physical characteristics of the object.

 Effectively, nowhere he says or even suggests that black holes are made of "classical ideal monoatomic gasses". He uses the simple case of an ideal gas for illustrating the difference between c and C.
And in the current situation "c" is irrelevant. What matters is C.

And in the case of black holes the physical material gets crushed to a singularity in a finite time leaving behind only the gravitational field whose thermodynamic properties are not constrained by the limits that constrain physical objects. Black holes are dominated by the gravitational field so if you add energy, the field will reconfigure itself, and that's what you are observe.

The problem is that the author is used to laboratory thermodynamics in which you don't have to worry about the energy of the gravitational field, which works very badly when you figure out the thermodynamics of objects which are dominated by gravity. So in doing the energy calculations, he is completely ignoring gravity, which results in conclusions that are ridiculous.
P: 476
 Quote by jambaugh I note in the paper he also invokes a strong form of the 3rd law, $\lim_{T\to 0}S = 0$. This form ignores residual entropy due to a degenerate ground state. He is here ignoring degeneracy. His reasoning may be implicitly the "no hair" theorem but that doesn't apply. The very debate, whether BH's evaporate, is a question of observing "internal" degrees of freedom in the configurations of emitted thermal radiation (here "internal" to the surface configuration?). Reading the short paper, he is invoking analogue physical systems (partitioned volumes, ideal gasses) without any direct thought experiments about a BH per se. I don't see the paper pointing out any physical contradictions, only the exceptional behavior of BH thermodynamics.
I was said in my thermo course that residual entropies are the result of ignoring some interaction that breaks the degeneracy. I.e. that those degeneracies are fictitious. In any case I cannot see how substituting the strong form by the weak form $\lim_{T\to 0}S = S_0$ changes anything for BH thermo.

How do you adjust the 'exceptional behaviour' of evaporating BHs with the thermodynamic properties of the supposedly emitted thermal radiation?
P: 476
 Quote by twofish-quant You add energy, the gravitational field rearranges itself and you get a different temperature. C is a quantity that includes both the effects of gravity and the physical characteristics of the object.
If you confound internal energy with rest energy or with some other kind of energy then C can contain everything you want, but then better calls it X.

 Quote by twofish-quant And in the current situation "c" is irrelevant. What matters is C.
But as the author emphasizes C is not c. The non-numbered equation before (6) implies dE=CdT, but that is different from (7). Many people believes that C is the heat capacity, but for an open system dE ≠ dQ.

 Quote by twofish-quant And in the case of black holes the physical material gets crushed to a singularity in a finite time leaving behind only the gravitational field whose thermodynamic properties are not constrained by the limits that constrain physical objects. Black holes are dominated by the gravitational field so if you add energy, the field will reconfigure itself, and that's what you are observe. The problem is that the author is used to laboratory thermodynamics in which you don't have to worry about the energy of the gravitational field, which works very badly when you figure out the thermodynamics of objects which are dominated by gravity. So in doing the energy calculations, he is completely ignoring gravity, which results in conclusions that are ridiculous.
Not only it seems that you have not studied enough thermo, but you did not even read #12, where such claims were corrected.
P: 6,863
 Quote by juanrga If you confound internal energy with rest energy or with some other kind of energy then C can contain everything you want, but then better calls it X.
This gets into definitional issues, but when astrophysicists talk about black holes and stars or whatever, they are indeed talking about C.

 But as the author emphasizes C is not c. The non-numbered equation before (6) implies dE=CdT, but that is different from (7). Many people believes that C is the heat capacity, but for an open system dE ≠ dQ.
When you dump energy into a black hole or star, some of that energy goes into the gravitational field that effects the thermodynamics of the object. You can define a "heat capacity" based the interaction of the system to additional energy.

Also, a non-radiating star or black hole is a closed system.

 Not only it seems that you have not studied enough thermo, but you did not even read #12, where such claims were corrected.
And that "correction" is wrong. The basic problem I have with the entire paper is that he is using energy balance arguments. When you use energy balance arguments in astrophysical objects, you have to take into account the interaction of the gravity field. If you don't, then none of your results make any sense. Essentially, he writes an entire paper about black holes, and not once does he mention the word "gravity", and nowhere does anything approaching gravity enter into any equations.

If you can come up with an argument in which you can argue that it's possible to talk about black holes while ignoring gravity, I'd like to hear it.
P: 6,863
 Quote by juanrga It is evident that this kind or argument can be inverted. People as Hawking, experienced in black holes and general relativity, can say nonsense when entering in the field of thermodynamics.
Exactly. That's why argument to authority fails. In this situation, I think Hawking is right.

 Even if we ignore now that «the energy that is in the gravity field» is not well-defined in general relativity, what you say about thermodynamic energy and gravitation seems to be without any basis.
It's pretty simple. Gravitational potential energy makes up a substantial amount of energy in astrophysical objects. Hence arguments based on energy conservation that ignore interactions of the gravity field just don't work. If you introduce the gravity field, the situation that Hawking finds is pretty standard.

 Already many ordinary textbooks explain how gravitational energy $M\phi$ contributes to thermodynamic energy. Of course, in a BH the situation is more complex and $M\phi$ is not enough, but thermodynamics in presence of gravitation continues to hold and I fail to see your point.
My point is that adding gravitation introduces additional terms into the energy equation, and once you introduce those terms, the arguments in the paper break down. The paper makes arguments that ignores the impact of gravity on the thermodynamic equations, and you just can't do that.

Gravity changes everything. Once you have a gravitational field, then adding or removing energy from the system will cause interactions with the gravitational field, and *that's* what gives you heat capacities that you don't see in non-self gravitating objects.

Black holes are not monoatomic ideal gasses. Because of self-gravitation, black holes are different enough so that you can't even use monoatomic ideal gasses as an analogy.
 Sci Advisor PF Gold P: 4,775 Of interest to discussion of entropy of self gravitating systems is the following essay. Of particular interest is the discussion of gravothermal catastrophe - that self gravitating systems really have no equilibrium point short of a black hole. This essay is not relevant to the core question of the validity of Bekenstein-Hawking entropy. It takes that as a given, and argues that this is exceptional and not some natural limit of ordinary gravitational collapse processes. http://philsci-archive.pitt.edu/4744...nt_archive.pdf

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