Question about the Entropy of a Black Hole Singularity

[ShadowX5452]

TL;DR Summary

This is a question to figure out if the Entropy of a Black Hole can only be found on the Event Horizon, or if it may exist in the singularity

Hello,
I'm new here and my field of studies is not about science so forgive me if I say something that appears to be an abomination!

I have a YouTube channel and I'm writing the script for a video that will use the laws of physics and quantum mechanics to explain the lore from a videogame. Despite the end product of my questions here today, what's really important is my desire to understand and learn what I'll be asking about, which is something I would have eventually faced even without this videogame, since I've always loved learning about the universe and the science behind it.

My research began with entropy and, after a few days, I feel like I finally got an understanding of it.
Where my research caused doubts, is when entropy is applied to black holes, Hawking radiation and the black hole information paradox.
I do understand that there isn't a solution to the paradox yet, so I'm obviously not asking for it here, but there's something that's been bothering me.

Everytime I've researched entropy about black holes, I've always only found about how it's calculated on the surface of the even horizon, reason why black holes have the most entropy in the universe, but I haven't found anything about their singularity.

According to the past hypothesis, in the early stages of the universe, when the Big Bang happened, there was the lowest concentration of entropy, simply because the universe moves on the arrow of time and it should be going forward toward maximum entropy, so looking back to the past, the universe should have low entropy as a consequence. This low entropy of the early universe can also be explained because of the gravitational forces that kept everything clamped together, which is not a likely state, hence low entropy.

As far as I know, hoping this is not where the problem lies, when a massive enough star reaches its end, it can't fight against its own mass and it collapses on itself into a single point, a singularity, which has such an extreme gravitational pull that not even light can escape it.
This also creates an event horizon, the boundary past which gravity is too much to escape, and an accretion disk with everything that closely orbits the black hole.

Now, the information paradox exists simply because the information of an object can't be deleted out of existence, which is the conservation of quantum information. Everything should be reversible, so from the end result, we should be able to understand the original state, which seems to fail when it comes to Black Holes. We apparently lose the information of whatever falls into a black hole, especially considering that black holes evaporate over time until they cease to exist.

Stephen Hawking then discovered that black holes release radiation, the hawking radiation, which is thermal radiation, so it shouldn't carry information but just heat or temperature (not sure what's the right term here).
From here on out, I've read of Imaginary space, black holes being connected by "islands" that retain that information, wormholes that either send information to another black hole (but how could that solve the problem?) or send information from inside the black hole past its event horizon, I mean, there are countless theories.

But what about the singularity of the black hole?
Isn't that, more or less, the same as the beginning of the universe? To me, ignorant as I am, it sounds like a point with extreme gravity that keeps everything clamped together in an unlikely state, so low entropy. Couldn't the information have been simply pulled into the singularity, where it would stay until the black hole will have inevitably evaporated, exposing the singularity and causing something like a Big Bang, and explosion that would release everything, information included, back into the universe?
In this case, the information wouldn't have been lost, it would have simply been in a place that's completely inaccessible to us, at least with our current means.

I do realize that the gap in my knowledge can't be bridged by reading articles and watching videos made by physicists, so my conclusions may very well be astronomically stupid, which is the reason why I decided to turn to experts in the fields, also to avoid embarrassing myself with my YouTube video.

I hope it wasn't too dumb of a question! If you decide to respond, thank you very much!

 

[PeterDonis]

I've always only found about how it's calculated on the surface of the even horizon

It's not that it's calculated "on" the horizon, as if it were "located" there; it's just that the entropy is proportional to the area of the horizon. The entropy isn't "located" in any particular place; it's an overall property of the hole.

I've read of Imaginary space, black holes being connected by "islands" that retain that information, wormholes that either send information to another black hole (but how could that solve the problem?) or send information from inside the black hole past its event horizon, I mean, there are countless theories.

None of this is relevant to your actual question. There are lots of speculations out there, but that doesn't mean they're worth spending time worrying about.

what about the singularity of the black hole?
Isn't that, more or less, the same as the beginning of the universe?

No.

it sounds like a point with extreme gravity that keeps everything clamped together in an unlikely state, so low entropy.

No, that's not what the black hole singularity is. It's a moment of time which is to your future if you're anywhere inside the horizon. It's not a place in space. Nor is it the location of the hole's gravity; the hole's gravity is a global property of its spacetime geometry. The singularity is not the "source" of the gravity.

Couldn't the information have been simply pulled into the singularity, where it would stay until the black hole will have inevitably evaporated, exposing the singularity and causing something like a Big Bang, and explosion that would release everything, information included, back into the universe?

No. As I said above, there are plenty of speculations out there, but this is not one of them.

 

[ShadowX5452]

It's not that it's calculated "on" the horizon, as if it were "located" there; it's just that the entropy is proportional to the area of the horizon. The entropy isn't "located" in any particular place; it's an overall property of the hole.


None of this is relevant to your actual question. There are lots of speculations out there, but that doesn't mean they're worth spending time worrying about.


No.


No, that's not what the black hole singularity is. It's a moment of time which is to your future if you're anywhere inside the horizon. It's not a place in space. Nor is it the location of the hole's gravity; the hole's gravity is a global property of its spacetime geometry. The singularity is not the "source" of the gravity.


No. As I said above, there are plenty of speculations out there, but this is not one of them.

I suppose this means that I should make more research about the singularity to really understand what it is.

As someone not from this field of study, a moment of time which is to my future if I'm inside a black hole, is obviously hard to understand, because I lack the underlying knowledge that makes this statement make sense.

Though, I wonder at this point, is the mass of the dead star part of the information the paradox can't find? I mean, it collapsed on itself (at least I hope that's right at least), but where is it?

My wrong understanding of a singularity comes from what I've been taught in school about it, which is a star collapsing into a singularity, which is clearly wrong from your answer.

As for the countless theories that don't really explain the information paradox, although they're not the focus of my question, they do have something to do with what I'm writing, that's why I read them, but yes, it's nit the focus of this specific question.

Thank you for your reply!

 

[PeterDonis]

a moment of time which is to my future if I'm inside a black hole, is obviously hard to understand

It means that once you're inside the hole, your future is guaranteed to have a limited duration. Your wristwatch only has a finite number of ticks left before you reach the singularity and are destroyed. At least, that's what the classical GR model says. See further comments below.

is the mass of the dead star part of the information the paradox can't find?

In classical GR models, yes. The collapsed star ends up inside the hole and its information never comes out; it gets destroyed when it hits the singularity. See further comments below.

I mean, it collapsed on itself (at least I hope that's right at least)

Yes.

where is it?

According to classical GR, it gets destroyed in the singularity--because the singularity destroys everything that reaches it. Just like you if you fall into the hole, once the collapsing star is small enough that its surface area is less than the area of the event horizon of the hole, its future is limited as I described above. Clocks riding with the collapsed matter only have a finite number of ticks before they reach the singularity and are destroyed along with the star.

My wrong understanding of a singularity comes from what I've been taught in school about it, which is a star collapsing into a singularity, which is clearly wrong from your answer.

If by "collapsing into a singularity" you mean "collapsing into a point in space that then remains inside the hole forever", then yes, you're correct that that's not what happens.

 

[PeterDonis]

Moderator's note: Thread moved to relativity forum.

 

[ShadowX5452]

It means that once you're inside the hole, your future is guaranteed to have a limited duration. Your wristwatch only has a finite number of ticks left before you reach the singularity and are destroyed. At least, that's what the classical GR model says. See further comments below.


In classical GR models, yes. The collapsed star ends up inside the hole and its information never comes out; it gets destroyed when it hits the singularity. See further comments below.


Yes.


According to classical GR, it gets destroyed in the singularity--because the singularity destroys everything that reaches it. Just like you if you fall into the hole, once the collapsing star is small enough that its surface area is less than the area of the event horizon of the hole, its future is limited as I described above. Clocks riding with the collapsed matter only have a finite number of ticks before they reach the singularity and are destroyed along with the star.


If by "collapsing into a singularity" you mean "collapsing into a point in space that then remains inside the hole forever", then yes, you're correct that that's not what happens.

But wouldn't this explanation go against the law that says that nothing is created nor destroyed?
I suppose this is where the paradox begins and why quantum mechanics is involved, but still can't find a solution, right?

 

[phinds]

But wouldn't this explanation go against the law that says that nothing is created nor destroyed?

Huh? Things are created and destroyed all time. Can you clarify what you are asking?

 

[phinds]

I suppose this means that I should make more research about the singularity to really understand what it is.

"singularity" is a place-holder term, standing in for the phrase "the place where our model(s) break down and we don't know WHAT is/was happening.

If you are talking about inside a black hole, we won't know fully what's going on their until we have a theory of quantum gravity.

 

[ShadowX5452]

Huh? Things are created and destroyed all time. Can you clarify what you are asking?

Doesn't the law of conservation of mass say that nothing is created and nothing is destroyed? Doesn't this also apply to quantum physics when it comes to information that should never be able to be destroyed?
I mean, if things can be completely destroyed, then why would the black hole information paradox exist to begin with?

 

[phinds]

Doesn't the law of conservation of mass say that nothing is created and nothing is destroyed?

For closed systems, the total energy inside the system, absent any external forces, will remain constant, but mass can be destroyed by turning into radiation ("energy") and as long as it all stays inside the closed system, the overall energy remains constant.

The pure "law of conservation of mass" is for chemical reactions where matter just changes form (e.g. solid to gas)

 

[ShadowX5452]

For closed systems, the total energy inside the system, absent any external forces, will remain constant, but mass can be destroyed by turning into radiation ("energy") and as long as it all stays inside the closed system, the overall energy remains constant.

The pure "law of conservation of mass" is for chemical reactions where matter just changes form (e.g. solid to gas)

So this destruction is a conversion from mass to energy, and I suppose the closed system is the black hole in this case, right?
So what about the information about that object? I would imagine that simply saying that it has been destroyed, would go against time-reversal symmetry and conservation of information, so unitarity in quantum mechanics.
Does it simply mean that the information about an object that falls into a black hole or even the star that collapsed to form said black hole, still exists but we simply don't know where it is or how it can be retrieved in order not to defy the non-negotiable statements of quantum mechanics?

I'm sorry if I keep asking questions, but leaving this topic half understood, would invalidate the reason why I decided to ask about it in the first place, but also thank you for keeping up with my questions

 

[PeterDonis]

wouldn't this explanation go against the law that says that nothing is created nor destroyed?

No. The singularity itself, at $r = 0$, is not actually part of the spacetime. The law about "nothing is created or destroyed", as far as classical GR is concerned, means that stress-energy is conserved everywhere that is part of the spacetime. The issue with the singularity is that the spacetime itself ends there. We say things get "destroyed" there because the singularity is in the future for anything that falls into the hole, but when you actually look at the physics, it's just that the spacetime ends; there is no "destruction" process.

in order not to defy the non-negotiable statements of quantum mechanics?

We don't know that the QM law about not creating or destroying information is actually non-negotiable. That law is a different law from the classical GR law I described above. Our best current belief is that both classical GR and what we now know as QM are emergent from some deeper theory, probably some sort of quantum gravity. But we don't know what that deeper theory is or what it says, so we don't know how any apparent discrepancies between our current QM and our current GR will end up being resolved.

Proponents of the QM side of the "black hole war" (Susskind's term for the controversy over how the black hole information paradox is to be resolved) like to claim that the QM law is non-negotiable, but they don't know that. That's just their opinion.

 

[PeterDonis]

For closed systems, the total energy inside the system, absent any external forces, will remain constant, but mass can be destroyed by turning into radiation ("energy") and as long as it all stays inside the closed system, the overall energy remains constant.

The pure "law of conservation of mass" is for chemical reactions where matter just changes form (e.g. solid to gas)

Neither of these are actually relevant when considering what happens at the singularity in the classical GR model. The relevant law is the local conservation of stress-energy, which is different from both of the laws you state in the quote above.

 

[Vanadium 50]

"singularity" is a place-holder term, standing in for the phrase "the place where our model(s) break down and we don't know WHAT is/was happening.

The word "place" is unfortunate, as it really isn't even a place, much less "a p;ace where". In some respects it is more of a when than a where. It os a place only in the sense of "this place in the equation" or maybe "this place in the story."

 

[ShadowX5452]

So in the end, the singularity, which is not a place but an inevitable moment in time, has nothing to do with whatever happens to an object that falls into a black hole, except for marking the moment in which it ends.
A branch of science has no problem whatsoever with an object being destroyed, another branch of science believes information must be preserved, but even then, it's not necessarily accurate, at least for the first branch of science.
Basically, no one knows, some have ideas, and others don't really believe in them.

So, is this a situation in which one should just pick which branch makes more sense on an individual point of view, just like a person decides whether to study general relativity or quantum mechanics?

 

[PeterDonis]

the singularity, which is not a place but an inevitable moment in time, has nothing to do with whatever happens to an object that falls into a black hole, except for marking the moment in which it ends

Basically, yes, that's what the classical GR model is saying.

A branch of science has no problem whatsoever with an object being destroyed

As I've already said, that is not what the classical GR model is saying.

Basically, no one knows, some have ideas, and others don't really believe in them.

More or less, yes.

is this a situation in which one should just pick which branch makes more sense on an individual point of view, just like a person decides whether to study general relativity or quantum mechanics?

No. It's a situation where we are talking about a regime in which our current science simply doesn't tell us anything useful. So we just need to wait until science has advanced further. It's not like you have to take a position on the matter for any practical purpose. Just accept that right now we don't know what happens in this regime and leave it at that.

 

[Ibix]

So in the end, the singularity, which is not a place but an inevitable moment in time, has nothing to do with whatever happens to an object that falls into a black hole, except for marking the moment in which it ends.

I would say the singularities you find in GR are edges of the model - in this case an "end of time" at a finite distance along the future of the black hole interior. Things in the model that reach there are not in the model any more.

But it's important to note that this is a prediction of the model in a region we can't directly test, where gravitational strength is as far from how it is in the regions we're familiar with as it can be. Just as Newtonian gravity turned out to be not quite right (actually only an approximation to GR) when we studied more extreme circumstances than Newton could, it's likely that GR is not quite right and only an approximation to something more complicated. The difficulty of making GR and quantum theory play nicely together is probably one of the hints of that. Unfortunately, we haven't yet worked out what it's hinting at, so the best we can do is point out that there are limits to our knowledge.

 

[bahamagreen]

When you started with entropy, did you run across Don Page's argument that "...if a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared."?
Wikipedia - Black hole information paradox