All Questions
Tagged with black-holes entropy
136 questions
4
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Proof of Bekenstein bound
I am trying to find a student-friendly (but mathematically rigorous) proof of the Bekenstein bound. Unfortunately, all the proofs I have found are too complicated to understand (most of them refer to ...
- 159
4
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1
answer
102
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Why some authors interpret the action in the Euclidean signature as a measure of entropy?
In discussions of the black hole information paradox, I've encountered literature suggesting that some authors interpret the action in the Euclidean signature as a measure of entropy. Could you ...
- 219
4
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2
answers
212
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What is the upper bound for black hole entropy derived from in the Bekenstein bound?
From several unrelated sources (such as Scott Aaronson's discussion of hypercomputation or this article about a bound on the number of degrees of freedom of any theory with a positive cosmological ...
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2
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1
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118
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Two questions about the expansion of the universe and matter?
I have a couple of questions about the consequences that the expansion of the universe (being an accelerated expansion or a linear one) would have on matter and structures in the universe
1. Neutrinos:...
- 2,878
3
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1
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106
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Different Bekenstein bound equations – what’s the difference?
Can someone help me understand the difference between the Beckenstein bound equations that I’ve come across? They all appear to have different dimensions.
I’ve been told that if you include the ...
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4
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0
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71
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Generalized entropy of black holes
In the review paper 2006.06872 by Maldacena, in eq.(2.4) they wrote that the total entropy of a black hole and its environment also has a contribution from the quantum fields outside the horizon which ...
- 512
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0
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60
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The Formula For Entanglement Entropy of an Evaporating Black Hole
I am trying to find a proof for the formula for entanglement entropy of an evaporating Black Hole. It is introduced and used in many papers such as The entropy of Hawking radiation, by Ahmed Almheiri, ...
- 219
2
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Calculating the Bekenstein-Hawking entropy for 1+1 black hole with dilaton background
According to this paper the Bekenstein-Hawking entropy of a 1+1 black hole which described by the $SL_k(2,\mathbb{R})/U(1)$ WZW cigar geometry is given by the following formula appearing in eq. (5.7):
...
1
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1
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Is the Ryu-Takayanagi (RT) formula calculating coarse-grained or fine-grained entropy?
I think it is computing the fine-grained entropy. However, I am confused by the case that when there is a black hole in the bulk. The Ryu-Takayanagi surface may include the horizon of the black hole ...
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1
vote
1
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63
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Derivation of area horizon law for $SAdS_5$ black hole
How can you derive the area horizon law of the $SAdS_5$ black hole? The metric is written as
$$ds_5^2=\frac{L^2}{z^2}[-fdt^2+dx_1^2+dx_2^2+dx_3^2]+\frac{L^2}{z^2}f^{-1}dz^2$$ where $f(z)=1-z^4/z_H^4$
...
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2
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114
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What is the meaning of "The volume inside a black hole always increases"?
I have been following recent work by Susskind [1,2] where he talks about fact that the volume inside an eternal black hole increases with time. I am unsure how to obtain this result. I'll show my ...
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Entanglement entropy as the source of Bekenstein-Hawking entropy
I think I'm missing something about interpreting a black hole's entanglement entropy as the source of it's Bekenstein-Hawking entropy, and I can't find any literature on it.
So, we know that our ...
- 31
1
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1
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295
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Could any new structures be formed after the heat death of the universe?
When the universe would reach a maximal state of entropy, heat death would presumably be reached and no structures would be left after the last black hole would evaporate.
However, is this really true?...
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2
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3
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513
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What is a black hole microstate?
What is the most generally accepted way of defining what a black hole microstate is? On a related note, I don't believe there is a Wikipedia page on the topic.
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2
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Does entropy decrease in the late universe? [duplicate]
The early universe had an entropy of $10^{88} k_B$ . This entropy does mostly come from photons, quarks and leptons and stayed constant over time, due to adiabatic expansion.
Sagittarius A* has an ...
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1
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Why black hole erase information
It is usually said that according to the no hair theorem, black holes erase the information enter them which reduce the entropy and imply the so called "information paradox".
The problem is ...
- 1,774
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How to calculate the total entropy of dS black holes?
In several articles where the thermodynamics of dS black holes have been investigated, the entropy part of the model or the total entropy has been analyzed based on the entropy of the black hole ...
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1
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1
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What happens to the entropy of the pre-existing information on a black hole event horizon as more mass falls into the hole?
Does the old entropy stay the same as new bits of information are added to increase the overall entropy?
user355436
1
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0
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96
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How is $S=\frac{A}{4G}$ not manifestly a solution to the black hole information paradox?
If we take the black hole entropy $S=\frac{A}{4G}$ as given and let the black hole evaporate, the area of the black hole decreases, so the entropy of the black hole decreases. The entropy should tell ...
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2
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2
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106
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Will a black hole disappear?
Reading The brief history of time by Stephen Hawking and the chapter 7 BLACK HOLES AIN’T SO BLACK has below.
Does it mean if his theory is correct, a black hall can disappear on its own?
Because ...
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2
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264
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What does the no-hair theorem state about the entropy of black holes?
So does the no hair theorem say that all classical black holes will have zero entropy? If yes, why?
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3
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1
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202
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Conceptually, why is the entropy of black hole related to Planck length?
I was watching a lecture on the holographic principle, and it presented the equation for the entropy of a black hole as $$S_{BH} = \frac{A}{4l_p^2}$$ My question is why, conceptually, the entropy of a ...
- 1,397
4
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Quantum extremal surface and black hole evaporation inquiry
Recently there has been progress made in the black hole information paradox by using the tools of AdS-CFT correspondance. Specifically, the Page curve for an evaporating black hole has been ...
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Gravitational path integral derivation of black hole temperature and entropy
Using the gravitational path integral we can define the partition function as:
$$
Z(\beta) = \int\mathcal{D}g\mathcal{D}\phi e^{-I_E[g,\phi]}
$$
with boundary conditions:
$$
t_E \sim t_E + \beta, \...
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2
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117
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Do black hole horizons always increase?
In asymptotically flat spacetimes, the area of a black hole event horizon must always increase, provided the Null Convergence Condition is followed ($R_{\mu\nu}k^{\mu}k^{\nu}\geq0$ for all null ...
2
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2
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404
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Technical review article on black hole thermodynamics?
Can anyone recommend a resource on black hole thermodynamics for physicists who are not familiar with this area? I'd like to see a rough sketch of the derivations of black hole entropy and Hawking ...
2
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0
answers
36
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Geometric Entropy & the Partition Function for Conical Deficits
In their paper, Callan and Wilczek claim to derive from the thermal entropy
$$S_\text{thermal} = -\left(\beta\frac{\partial}{\partial\beta}-1\right)\ln(\mathcal{Z})$$
a geometric entropy which is ...
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2
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119
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Is formation of a black hole thermodynamically favourable?
Isn't it like that the black hole is just swallowing suns and other parts of cosmos, and thus continuously absorbing matter. I know that it emits radiations also, which should be negligible in terms ...
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350
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Is there a black-hole information equation?
According to some sources, black-hole information is proportionate to the surface area, and, the equation trotted out is $$S = \frac{A k}{4 l_p^2}.$$ But according to another source, the entropy and ...
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Why must black hole have entropy?
From what I understand 2nd law of thermodynamics is just saying that information cannot be destroyed, ok got it. When a massive star collapses under it's own weight, it turns into a black hole and all ...
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2
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3
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371
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Why did people think that black holes have zero entropy before the works of Bekenstein and Hawking?
To the extent I know, before Bekenstein and Hawking, the general consensus among physicists was that the black holes have zero temperature and zero entropy. I can possibly understand why people would ...
- 12.3k
7
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1
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290
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Black hole horizon : entropy or surface tension?
Usually (from Hawking's calculations), a black hole has entropy defined by its horizon's area:
$$S = \frac{A}{4G}, \tag{1}$$
where $A = 4 \pi r_H^2$ is the area. From thermodynamics:
$$dE \equiv dM = ...
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Is the entropy of a black hole relative?
I have a question about the entropy of black holes. Well, some time ago I was able to demonstrate theoretically that the entropy of black holes should be relative, that is, depend on the observer.
But ...
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1
answer
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Is entropy of planets and others bodies proportional to the area?
Is entropy of planets and others bodies proportional to the area? If yes, how do I prove that? I know it works for a black hole but, and for others? If no, then the entropy is really proportional to ...
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Micro black-hole microstates [closed]
If we compute the number of microstates in a black-hole of Planck radius using the Bekenstein–Hawking (BH) formula we get $\exp(\pi/4)$. Maybe it was too optimistic to expect an integer, but ...
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Child Universes
I was watching a program on the future of the Universe and it got into the eventual heat death resulting from Hawking Radiation as the last hurdle till nothingness (assuming the unproven theory of ...
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6
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Introductory References for the Black Hole Information Paradox
I am looking for introductory references for the Black Hole Information Paradox and trying to compile a sequential list through which someone familiar with the basics of QFT and GR can go to ...
-3
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2
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471
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How does String Theory calculate the entropy of a black hole in a background-dependent way?
How does string theory get an agreement to the Hawking-Bekenstein equations to calculate the quantum entropy of a black hole in a background-dependent way?
Is there any sort of area parameter in ...
1
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0
answers
377
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Are Black Holes high and low entropy?
Some time ago I read that without knowing more about quantum gravity
the assumption that Black Holes continue to collapse is valid.
That mystifies me somewhat but for the purpose of this question I’m ...
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0
answers
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Thermodynamics of RN black holes [duplicate]
The RN metric in asymptotically flat spacetime is given here: Wikipedia page on RN metric.
From the metric, we can work out the Bekenstein-Hawking entropy to be S = Area/4 , which explicitly would be:...
- 1,202
1
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1
answer
140
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Calculate entropy of a sphere (?)
I saw these two videos (1 and 2) and in both of them Tony Padilla gives basically the same definition of maximum entropy in a region of space (a sphere). Now, searching the web I haven't found any ...
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Bekenstein–Hawking entropy: the proportionality constant and the 2D black hole
The Bekenstein–Hawking entropy is defined by the relation
$$S=\frac{k_BA}{4l_p^2},$$
where $k_B$ is the Boltzmann constant and $A$ is the area of the black hole's event horizon in units of the ...
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0
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Is Bekenstein-Hawking black hole entropy the maximum bound of the entropy of a black hole?
Is the entropy $S_{BH}=\frac{c^3 A}{4Gh}$, where A is the surface area of the event horizon of a black hole, the "real" entropy of the black hole or a maximum bound of that "real" entropy?
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Can black holes prevent heat death?
I recently learnt that black holes possess among the highest amounts of entropy in the universe. I might have stretched the idea preposterously far, but is it possible that this might be one of the ...
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1
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Do the logarithmic corrections to black hole entropy imply corrections to their energy or temperature?
Could somebody help guide the thinking in this situation?
Do the corrections to entropy $S$, like those of https://arxiv.org/abs/hep-th/0111001, affect the temperature of a black hole, or its mass, ...
- 684
4
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2
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3k
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Why does a black hole have much entropy?
Is that just an assumption by Bekenstein etc? For example, what is the different states a non-rotating primordial black hole can be in?
- 151
3
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1
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128
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Why is the temperature of a black hole given by $T=E/2S$?
Naively, I would imagine that
$$
T = \frac{E}{S}
$$
However, for a black hole, $E=c^4 R / 2G$ and $S= A k c^3 / 4 G \hbar $, which yields
$$
T = \frac{E}{2S}
$$
Is there a simple explanation for the ...
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2
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106
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What is the Equation? [closed]
I am refreshing my Physics skills and I cannot remember what this equation is. Will someone please tell me what this formula is for? It sort of looks like Stephen Hawkings equation for black holes.
$$...
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0
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106
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Event horizon area and entropy content of a black hole
I am aware that the entropy content of a black hole is proportional to the area of its event horizon, and that this can be boiled down to the bit content of a Planck area on the horizon, but I have ...
- 97.8k
2
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2
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2nd law of thermodynamics inside an event horizon?
Since time and space switch roles inside a black hole, does entropy inside a black hole still need to increase?
If not, maybe something very strange could pop into existence, only to be crushed ...
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