Black hole questions

[EdwardRo]

TL;DR

Random blackhole questions.

To start off, please understand that as much as I love physics and try to keep myself immersed in everything, my education in it doesn't extend past high school courses. I'm aware that I have a lot of holes in my knowledge and understanding, so please be gentil with me.

Today I was watching an episode from the world science festival on YouTube about black holes. I was letting the information mull around in my brain when I realized a few things...

1. Has anyone ever tried to build a black hole from the inside out?
I come from an engineering background, and sometimes you need to build things in reverse to get them to work.
What if you started at the plank length, determine the maximum amount of mass/energy that could be contained in that space. Then you can expand that out to cu mm, cu cm, cu m. That would then give you the minimum size the singularly would be.

2. If we imagine the singularly as a sphere, could there be a space within it where the gravity of the outer "crust" and inner core balance out? This could potentially create a zone within the singularly itself where it is re exposed to normal space time.
I'm thinking that if yes, then this could help explain the information paradox created.

Are these valid lines of thought? Where are the holes in my understanding?

 

[Ibix]

1. Has anyone ever tried to build a black hole from the inside out?
I come from an engineering background, and sometimes you need to build things in reverse to get them to work.
What if you started at the plank length, determine the maximum amount of mass/energy that could be contained in that space. Then you can expand that out to cu mm, cu cm, cu m. That would then give you the minimum size the singularly would be.

Classically, a black hole can have any size. There's a minimum mass for one to form by stellar collapse, because smaller stars don't leave enough mass in their remnants to collapse under their own weight, but smaller black holes (including microscopic ones) that formed in the early universe have been hypothesised. We've never seen evidence of them, though.

The singularity doesn't have a size. It's a breakdown of the model and lies outside the manifold, which is the entity that provides notions of things like size. We assume a working theory of quantum gravity will explain what actually happens where classical gravity fails.

2. If we imagine the singularly as a sphere,

The singularity is more like a moment in time than a place in space. It isn't anything like a sphere.

 

[Ibix]

2. If we imagine the singularly as a sphere, could there be a space within it where the gravity

On a re-read, are you using "singularity" and "black hole" as synonyms? They're not the same thing. The singularity is inside the black hole, but it is not all of it.

could there be a space within it where the gravity of the outer "crust" and inner core balance out?

Nothing we are aware of can stop gravitational collapse once neutron degeneracy pressure is overcome. Black hole interiors are vacuum as far as we know - everything that enters them hits the singularity in short order and nothing can stop that.

 

[PeterDonis]

Has anyone ever tried to build a black hole from the inside out?

You can't, because a black hole is not made of anything you can build something from. A black hole is just spacetime geometry. It's not made of parts.

 

[PAllen]

Well I can think of a recipe for building one Just start accumulating cold iron filings in one place, continue till you’ve added about 2 to 3 solar masses. Voila, it will collapse to a black hole.

 

[Orodruin]

Well I can think of a recipe for building one Just start accumulating cold iron filings in one place, continue till you’ve added about 2 to 3 solar masses. Voila, it will collapse to a black hole.

That’s not starting from the singularity though

 

[EdwardRo]

The event horizon is a feature of spacetime yes.
But wouldn't the singularly still be made of something. I know that neutron stars squeeze neutrons into "pasta". My thought process is that within the event horizon itself, the singularity may be a sort of physical object, even if it's just strings and brains. Which is why I asked the question the way I did.

 

[EdwardRo]

The singularity is more like a moment in time than a place in space. It isn't anything like a sphere.

Right, the spacetime diagram flips. That part makes sense. And I realized that the math breaks when trying to look past the event horizon.
However there needs to be mass for the event horizon to continue to exist I would think. I'm thinking that while there might not be anything like quarks, the compression may squeeze it into pure energy. So I figured one could start at the plank scale and build it out from there.

 

[EdwardRo]

On a re-read, are you using "singularity" and "black hole" as synonyms? They're not the same thing. The singularity is inside the black hole, but it is not all of it.

Nothing we are aware of can stop gravitational collapse once neutron degeneracy pressure is overcome. Black hole interiors are vacuum as far as we know - everything that enters them hits the singularity in short order and nothing can stop that.

When I say black hole, I'm speaking about the event horizon itself.
Singularity is the object within the event horizon, the remnants of the star itself. The mass.

 

[PeterDonis]

wouldn't the singularly still be made of something

No. It's not even part of the spacetime.

My thought process is that within the event horizon itself, the singularity may be a sort of physical object

It's not.

the spacetime diagram flips

No, that's not correct. Look at a Kruskal diagram, as seen, for example, in this Insights article:

https://www.physicsforums.com/insights/schwarzschild-geometry-part-3/

No flipping anywhere.

the math breaks when trying to look past the event horizon.

No, that's not correct either. A particular coordinate chart can't cover the horizon or the region inside it. But that's not the math breaking. That's just the math telling you to use a different coordinate chart.

there needs to be mass for the event horizon to continue to exist I would think

This is not correct. The solution to the Einstein Field Equation that describes a black hole is a vacuum solution--no "mass" (stress-energy) is required.

When I say black hole, I'm speaking about the event horizon itself.

That's not how the term "black hole" is defined in physics. It's defined as the entire region of spacetime at and inside the event horizon.

Singularity is the object within the event horizon, the remnants of the star itself. The mass.

This is not correct. See above.

You seem to have a lot of misconceptions about black holes. I would strongly recommend reading the entire series of Insights articles of which the one I linked to above is the third. It also gives some references where you can learn more.

 

[EdwardRo]

No. It's not even part of the spacetime.


It's not.


No, that's not correct. Look at a Kruskal diagram, as seen, for example, in this Insights article:

https://www.physicsforums.com/insights/schwarzschild-geometry-part-3/

No flipping anywhere.


No, that's not correct either. A particular coordinate chart can't cover the horizon or the region inside it. But that's not the math breaking. That's just the math telling you to use a different coordinate chart.


This is not correct. The solution to the Einstein Field Equation that describes a black hole is a vacuum solution--no "mass" (stress-energy) is required.


That's not how the term "black hole" is defined in physics. It's defined as the entire region of spacetime at and inside the event horizon.


This is not correct. See above.

You seem to have a lot of misconceptions about black holes. I would strongly recommend reading the entire series of Insights articles of which the one I linked to above is the third. It also gives some references where you can learn more.

Yes, like I said, I have a lot of gaps in my knowledge.
First, I realized that my nomenclature is wrong. I wanted to clarify what I meant when I used each term.
Second, I think the diagram you linked is the one I was talking about. And object at rest continues to move along the time axis, when it moves it's time axis slows and moves toward the space axis the faster it goes. My understanding is that once you enter the event horizon, the diagram basically flips, so that any motion accelerates your movement along the time axis. Meaning that any motion within the event horizon only speeds up your "impact?" with whatever is at the center. Sorry if I totally botched that explanation. But am I thinking about it correctly?
My thought process is that since mass=energy, the collapse cannot get rid of the mass that created it, even if the matter is destroyed. So I thought if the energy is still there, then there might be a finite limite that can be contained within a given volume.
Thank you for the reply, the link, and your patience. I plan on reading the article tomorrow.

 

[EdwardRo]

The solution to the Einstein Field Equation that describes a black hole is a vacuum solution--no "mass" (stress-energy) is required.

This is fascinating to me. I had it beat into my head that matter and energy cannot be destroyed. When a star collapses, that mass needs to go somewhere.
If I'm understanding what you're saying, then the curving of spacetime is where the energy is, and the interior of the event horizon is a vacuum?
How does this work with hawking radiation then? My understanding with that is that the particle spawn in pairs, with one falling in and the other flying out. Is it just just pulling energy directly from the curvature?

I'm so glad I started this thread, I'm actually kinda giddy over your responses.

 

[PeterDonis]

First, I realized that my nomenclature is wrong. I wanted to clarify what I meant when I used each term.

And your clarifications showed that your usage was not correct, in the way I pointed out.

And object at rest continues to move along the time axis

In that spacetime diagram, an object "at rest" is not what you seem to be thinking. An object "at rest" in Kruskal coordinates has a worldline that's a vertical line in the diagram. In ordinary terms, such objects are falling into the black hole (albeit not on free-fall trajectories). They are not "hovering" at rest at a constant altitude. Objects "hovering" at rest at a constant altitude above the event horizon have worldlines that are hyperbolas, in the right "wedge" of the diagram.

when it moves it's time axis slows and moves toward the space axis the faster it goes.

This is wrong even as a description of what happens in flat spacetime in special relativity. It is even more wrong as a description of what is going on in the diagram I linked to.

My understanding is that once you enter the event horizon, the diagram basically flips

Your understanding is wrong. The diagram I linked to can show the entire process of an object falling from infinity, through the horizon, to the singularity, with no flipping anywhere--it all can be shown on the diagram exactly as it appears in the article.

am I thinking about it correctly?

No. See above.

My thought process is that since mass=energy, the collapse cannot get rid of the mass that created it, even if the matter is destroyed.

The black hole does have nonzero mass, even after the matter that collapsed to create it hits the singularity and is destroyed. The mass is a geometric property of the spacetime. It doesn't require any matter.

I realize this is counterintuitive. Welcome to GR.

 

[Ibix]

I had it beat into my head that matter and energy cannot be destroyed. When a star collapses, that mass needs to go somewhere.

In "realistic" models of collapsing stars in GR, the matter reaches the singularity and leaves our model. Its gravitational effect remains. As we've said, the singularity is not expected to be a real thing - it's a failure of the model. We do not expect the world to actually work that way.

If you want a more accurate description of the black hole interior where the matter doesn't just fall off the edge of the map (and, indeed, the map doesn't have an edge to fall off) you need a quantum theory of gravity. Unfortunately we don't have one.

 

[PeterDonis]

In "realistic" models of collapsing stars in GR, the matter reaches the singularity and leaves our model. Its gravitational effect remains. As we've said, the singularity is not expected to be a real thing - it's a failure of the model. We do not expect the world to actually work that way.

In the sense that we don't expect stress-energy to just disappear, that's true.

However, it's also true that we do expect a black hole to be "made of" vacuum, not stress-energy--or at least that's one very common expectation. There are strong heuristic arguments indicating that, while the spacetime model of classical GR might break down near the singularity, it should not break down in the rest of the black hole. Most of the spacetime region occupied by the hole should be describable by classical GR. And that includes the fact of it being vacuum, and the "mass" of the hole being a geometric property of the spacetime, not something due to any remnant of stress-energy from the collapsed object.

 

[PeroK]

Yes, like I said, I have a lot of gaps in my knowledge.
First, I realized that my nomenclature is wrong. I wanted to clarify what I meant when I used each term.
Second, I think the diagram you linked is the one I was talking about. And object at rest continues to move along the time axis, when it moves it's time axis slows and moves toward the space axis the faster it goes. My understanding is that once you enter the event horizon, the diagram basically flips, so that any motion accelerates your movement along the time axis. Meaning that any motion within the event horizon only speeds up your "impact?" with whatever is at the center. Sorry if I totally botched that explanation. But am I thinking about it correctly?

I would say that a black hole is about 4D geometry. There is no global "time" axis. In many ways, you need to free your mind of the simple concepts of classical motion.

My thought process is that since mass=energy, the collapse cannot get rid of the mass that created it, even if the matter is destroyed. So I thought if the energy is still there, then there might be a finite limite that can be contained within a given volume.
Thank you for the reply, the link, and your patience. I plan on reading the article tomorrow.

It might be helpful to realise that a black hole means two different things:

1) The Schwarzschild Black Hole is a mathematical solution in GR where there is no mass, no particles and no energy anywhere. It's a complete vacuum. All you have is spacetime. Nothing else. The geometry of spacetime, however, is characterised by a parameter, using denoted by $M$.

You can, however, introduce a small "test" particle into this spacetime (without significantly changing the spacetime geometry) and see what happens. By applying the laws of GR, the test particle "falls" toward the event horizon. As there is no universal, global time, it's best to use the proper time of the particle.

The particle, in finite proper time, passes through the event horizon. And, in a further finite proper time, the model ends - abruptly, you might say. This is because the Schwarzschild Black Hole has a mathematical singularity. The model breaks down and the lifetime of the particle ends, because the mathematical model end. There is no "centre" of the Black Hole, where the particle collides with anything. Quite literally, time just runs out for the particle. But, this is all a mathematical model.

2) A collapsing star of sufficient mass will eventually collapse in on itself and there are no known constraints to prevent its collapse. You could say that the star collapses into a something close to a pure Schwarzschild Black Hole. With the parameter $M$ being the residual mass of the star. What does appear to be clear, is that the star definitely collapses below the event horizon. There is evidence of that.

Again, however, this is a mathematical model for a stellar collapse. What eventually happens to the matter that falls below the event horizon that has formed is unknown. If we use the theory of GR, then eventually (in the proper time of the particles that make up the star), time runs out for the residual mass. Again, the model ends abruptly for those particles. In other words, the theory of GR breaks down.

This cannot, however, be a satisfactory physical model. We need a theory of quantum gravity (to replace or enhance GR in the region within the event horizon) in order to say what happens to the mass of the star.

You cannot understand this stuff by thinking about classical motion, forces, acceleration and classical time and space axes.

 

[PeterDonis]

What does appear to be clear, is that the star definitely collapses below the event horizon. There is evidence of that.

To be clear, we don't actually have evidence of an event horizon. We only have evidence of apparent horizons--very heuristically, regions where things fall in and nothing appears to come out. The only way to know for sure that these apparent horizons actually are (or more precisely are associated with) event horizons would be to know the entire future of the universe, because an event horizon is a global feature of the 4D spacetime geometry, so you have to know the entire 4D spacetime geometry to know for sure that the geometry has that feature.

The reason this is important is that, as has already been said in this thread, we expect that GR breaks down near the singularity, and that some kind of quantum gravity theory replaces it that doesn't have a singularity--that somehow makes the mass of the collapsing object go somewhere instead of just ceasing to exist. But it's extremely hard to find any viable model that does that, and still has an actual event horizon. The kinds of models one arrives at when one attempts to model how quantum gravity effects might change things, or at least the ones I've seen, end up having only apparent horizons--there are no actual event horizons, and the global causal structure is the same as that of Minkowski spacetime. (An example is the Bardeen black hole--"black hole" is a misnomer in this case--which has been discussed in some previous PF threads.) This kind of model also has the advantage of giving a simple solution to the black hole information paradox--there's no actual black hole (no actual event horizon), so no paradox--a model with this kind of causal structure has no problem maintaining quantum unitarity, for the same reason ordinary QFT models in flat spacetime have no problem with it.