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Isn't it like that the black hole is just swallowing suns and other parts of cosmos, and thus continuously absorbing matter. I know that it emits radiations also, which should be negligible in terms of the absorbed matter and thus energy. If the net internal energy of a black hole is just increasing and it's entropy being decreasing, then doesn't it's existence disfollow the laws of thermodynamics?

Níckolas Alves
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Abbas
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2 Answers2

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Intuitively, it might seem that black holes have low entropy, but that is not correct. Their entropy is in fact gargantuan. For example, as mentioned in the Scholarpedia entry for the Bekenstein–Hawking entropy,

Note that a one-solar mass Schwarzschild black hole has an horizon area of the same order as the municipal area of Atlanta or Chicago. Its entropy is about $4\times 10^{77}$, which is about twenty orders of magnitude larger than the thermodynamic entropy of the sun.

(See, e.g., this post for a bit on the entropy of the Sun).

Hence, black holes are actually quite favorable from a thermodynamic point of view, provided that there is a sufficiently high density so that the black hole can form. For example, Gibbons and Perry have considered the example of a black hole inside a box filled with radiation. If the density of energy in the box is not very large, then it is favourable for the radiation gas to exist alone, without a black hole. However, there is a turning point at which the density becomes high enough and a black hole condenses, having then roughly $97.7\%$ of the energy available in the box. I should point out, however, that the presence of Hawking radiation is extremely necessary for this argument, since that is what allows the black hole to be in thermal equilibrium with something. Furthermore, it is also essential in arguing what is the entropy of a black hole, as I explained in this post.

Níckolas Alves
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  • “I should point out, however, that the presence of Hawking radiation is extremely necessary for this argument” - Great point +1. The problem is that the Hawking radiation cannot exist without violating fundamental laws of nature, as expressed in the Information Paradox. Semiclassical gravity forcefully merges two incompatible theories, GR and QFT. The Hawking radiation is but a small artifact of not having the proper theory of Quantum Gravity to describe what actually happens at the horizon. And since this radiation cannot exist, the concept of entropy has no meaning for black holes. – safesphere Jan 18 '22 at 14:36
  • @safesphere I actually tend to disagree haha, but since the comments are not meant to discussion, I'll mention for other readers that since these are research-level topics, there is still a lot of ongoing debate on the interpretation of these results. As far as I know, safesphere's comment is perfectly compatible with current knowledge, but there are also other competent physicists (such as W. Unruh and R. Wald, afaik) who do not believe the Information Paradox to be a problem at all. – Níckolas Alves Jan 18 '22 at 14:53
  • Thanks for the link! Unruh is a very smart guy and the paper is a joy to read, but its analysis is not exhaustive and its conclusion is based on a number of unproven assumptions: (1) the existence of “quantum fluctuations”; (2) GR remaining classical at the quantum scales; (3) the existence of the interior spacetime “inside” a black hole; (3) the existence of the null infinity (referred to in the paper as “not a Cauchy surface”), which doesn’t exist in a closed universe. A great paper putting a lot of clarity on the subject, but very far from resolving the Information Paradox :) – safesphere Jan 18 '22 at 17:49
  • I am just a beginner in the field of thermodynamics , just knowing to solve simple problems of first and second law and you guys made your views impossible for me to understand . It's not good . – Abbas Jan 18 '22 at 17:52
  • @Abbas the question you asked actually has to do with much more than thermodynamics. The comments to this answer are a bit more related to other stuff and are not necessarily central to your question rn (except for the point safesphere mentioned that the existence or not of Hawking radiation is fundamental to the answer). Can you understand the answer I wrote itself or is it too cloudy as well? If so, can you pinpoint what you did not understand? (I believe the comments can still be interesting to other users reading this post later, though) – Níckolas Alves Jan 18 '22 at 21:27
  • @safesphere You're welcome! And I pretty much agree with your remarks on the paper's limitations. I guess there's no way of denying there's still a long way to go before the paradox is solved (or settled) =) – Níckolas Alves Jan 18 '22 at 21:30
  • The link you posted as "in this post" was very enjoyable and understandable for me. Perhaps not all questions have answers in similar tone , so I will learn more thermodynamics and physics and perhaps I will understand these stuffs one day like you guys . Thanks for the answers . – Abbas Jan 19 '22 at 05:31
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On the contrary, black holes are the objects in the universe with the highest entropy. According to the Hawking-Bekenstein formula, the entropy $S$ of a black hole is proportional to its surface $A$ which is by swallowing matter constantly increasing as does entropy:

$$ S= \frac{k_BA c^3 }{4 G\hbar }$$

using the usual constants as $c$ speed of light, $k_B$ Boltzmann's constant, $G$ gravitational constant and $\hbar$ Planck's constant.

So black holes fulfill perfectly the second law of thermodynamics and provide a huge contribution to the entropy of the universe.

Frederic Thomas
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