# Do black holes determine time's arrow?

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shlosmem
Does black holes determines time's arrow? Otherwise how to explain with time reversed objects been pushed out from black holes?

The maximally extended Schwarzschild black hole includes a black hole and a white hole. Under time reversal the black hole becomes the white hole and vice versa.

shlosmem
shlosmem
Does "white hole" can be explained by the standard physics? Let's say we have a mass that collapse to a black hole - now under time reversal we also have the same mass concentration, so it should become a black hole under the same gravitational rules, so what make it white?

Let's say we have a mass that collapse to a black hole - now under time reversal we also have the same mass concentration,
No - under time reversal, instead of a collapsing cloud of matter forming a black hole you have an expanding cloud of matter coming from a white hole with incoming radiation to warm it and expand it. You would not expect this to form a new hole, black or white.

The maximally extended Schwarzschild spacetime I spoke of is an eternal black hole. It didn't form from anything, which is why it needs a white hole to be plausible under time reversal.

shlosmem
You would not expect this to form a new hole, black or white.
Can you please explain it a bit more?
If white hole is not creating mass out of nothing, it means that until the "explosion" we had all the mass in a singular point. So why does gravity is not working here as expected?

Black hole singularities are not points. They are more like a moment in time, which is one way of explaining why you can't avoid them once you are inside the horizon.

If matter can hit a black hole singularity then matter can be emitted by a white hole singularity. Singularities don't really have a mass, but you could see it as the white hole singularity losing mass in the reverse of a black hole singularity gaining mass. However, the whole point of a singularity is that it's where our physical models have definitely gone wrong, so what happens there won't necessarily make sense. So a better way to put it is that whatever is actually where our models put a white hole singularity emits matter and radiation in a time-reverse of whatever is actually where our models put a black hole singularity.

SolarisOne
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Can you please explain it a bit more?
If white hole is not creating mass out of nothing, it means that until the "explosion" we had all the mass in a singular point. So why does gravity is not working here as expected?
Although your description is somewhat off as explained above, it is important to note that very often there are solutions to the equations of the laws of physics that are considered unphysical for one reason or another. This is one example. It is a mathematical solution that I don’t think anyone believes represents any part of the actual universe.

Drakkith and FactChecker
shlosmem
It is a mathematical solution that I don’t think anyone believes represents any part of the actual universe.
The question is whatever a white hole can actually be formed in our universe if somehow we were able to set all the particles in the right place. If the answer is "no" - it means black hole is setting time's arrow.

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The question is whatever a white hole can actually be formed in our universe if somehow we were able to set all the particles in the right place. If the answer is "no" - it means black hole is setting time's arrow.
Not really. A white hole is the initial condition, so you cannot set particles in the right place and have them evolve produce a white hole as a final condition. All you can do is to find one already existing naturally and see how it evolves.

Since its evolution would violate the 2nd law of thermodynamics, we don’t expect to see that naturally. But it is the 2nd law of thermo that is the issue, not the black/white hole. In other words, even here it is thermodynamics that provides the arrow of time.

SolarisOne and Ibix
The question is whatever a white hole can actually be formed in our universe if somehow we were able to set all the particles in the right place.
Black holes evaporate through Hawking radiation. So arrange time-reversed Hawking radiation and you'll get a time-reversed black hole.

Homework Helper
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The question is whatever a white hole can actually be formed in our universe if somehow we were able to set all the particles in the right place. If the answer is "no" - it means black hole is setting time's arrow.
To go back to the original question. I don't see the dependence of the arrow of time on black hole formation.

shlosmem
Not really. A white hole is the initial condition, so you cannot set particles in the right place and have them evolve produce a white hole as a final condition. All you can do is to find one already existing naturally and see how it evolves.
Let's say we have 2 holes, one is a black and the other is white. Both can have gravity fields (a satellite can orbit both bodies) , the difference between the two is that in the future the white will push out martials and disappear, but the black can become bigger and never push out martials.
The question is what is difference in the current internal state of these bodies that will make them so different in the future? Because from what I see, all we have is 2 identical bodies.

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Let's say we have 2 holes, one is a black and the other is white. Both can have gravity fields (a satellite can orbit both bodies) , the difference between the two is that in the future the white will push out martials and disappear, but the black can become bigger and never push out martials.
The question is what is difference in the current internal state of these bodies that will make them so different in the future? Because from what I see, all we have is 2 identical bodies.
The eternal black hole and white hole seem to be irrelevant to the question. They are part of the same maximally extended Schwartzschild solution. They are not things that evolve in our universe.

If you want to understand this Schwartzschild solution, you'll need to do quite a bit of research, as the whole solution and the white hole in particular are non trivial concepts.

The white hole is nothing like you are imagining!

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Let's say we have 2 holes, one is a black and the other is white. Both can have gravity fields (a satellite can orbit both bodies) , the difference between the two is that in the future the white will push out martials and disappear, but the black can become bigger and never push out martials.
The question is what is difference in the current internal state of these bodies that will make them so different in the future? Because from what I see, all we have is 2 identical bodies.
It doesn’t work this way at all. There are no 2 identical bodies.

A Schwarzschild black and white hole are not objects. They are two different moments in time for the same spacetime, the maximally extended Schwarzschild solution.

The difference between the black and white holes is that the white hole is the beginning of the spacetime and the black hole is the end. When you reverse it then what was the end becomes the beginning and vice versa.

SolarisOne
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I would like to point out that as far as spacetime geometry, there is no difference between a black hole and a white hole, if by "geometry" you mean topology plus spacetime curvature. The difference comes into play when you try to assign an arrow of time to each pair of timelike separated points. Two points in spacetime are timelike separated if it is possible for a slower-than-light observer (or other massive object) to travel between the points. If you choose an arrow of time so that for objects that are inside the event horizon of a black hole, the singularity is in the future, then consistency would require you to make the singularity of the white hole take place in the past. In the Schwarzschild geometry with both a black hole and a white hole, there are timelike paths that start at the white hole singularity and end at the black hole singularity. Which is the "start" and which is the "end" is purely conventional, until you introduce a thermodynamic arrow of time, as well.

Dale
shlosmem
It seems like you all treating black and white holes as spacetime topologies without paying attention to the cause of that topology which is the mass. We must have mass in order to have black hole and vise versa - a black hole means there is a mass inside. But if this is the case how does the same mass states causes 2 different behavior?

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It seems like you all treating black and white holes as spacetime topologies without paying attention to the cause of that topology which is the mass. We must have mass in order to have black hole and vise versa - a black hole means there is a mass inside. But if this is the case how does the same mass states causes 2 different behavior?
There is no cause (and can be no cause) for an eternal black hole. It is a spacetime geometry. It is not a black hole as formed by the collapse of a large star.

It seems like you all treating black and white holes as spacetime topologies without paying attention to the cause of that topology which is the mass.
Excuse me - I addressed this when I said:
Black holes evaporate through Hawking radiation. So arrange time-reversed Hawking radiation and you'll get a time-reversed black hole.
But if this is the case how does the same mass states causes 2 different behavior?
It doesn't. A collapsing gas cloud (precursor to a black hole) is not the same state as an expanding gas cloud (time reversed black hole final state).

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It seems like you all treating black and white holes as spacetime topologies
Not just topology, it is spacetime topology and curvature.

without paying attention to the cause of that topology which is the mass.
This is incorrect. A white hole is a feature of the maximally extended Schwarzschild spacetime, which is a vacuum solution. There is no mass anywhere in the manifold.

There may be white holes in other spacetimes that I am not aware of, where there is mass in the manifold. However, even if such spacetimes do exist the white hole cannot be caused by the mass or anything else since the white hole is literally the beginning of time. There is no part of the manifold before a white hole, nothing is before it so nothing can cause a white hole.

PeterDonis and Ibix
shlosmem
But if white hole has no mass , how come it has gravity? (Black hole can have a satellite , it means that on time reversed e.g. white hole will have also that satellite) .

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But if white hole has no mass , how come it has gravity? (Black hole can have a satellite , it means that on time reversed e.g. white hole will have also that satellite) .
https://en.wikipedia.org/wiki/White_hole

But if white hole has no mass
Who said it has no mass?

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But if white hole has no mass , how come it has gravity? (Black hole can have a satellite , it means that on time reversed e.g. white hole will have also that satellite) .
Gravity is more complicated than it is in Newtonian theory. In GR, there are non-trivial vacuum solutions, including the maximally extended Schwarzschild solution. A vacuum solution is one that describes a way that gravity can exist without any source.

In other words, spacetime can simply curve this way even without mass. That is what it means for something to be a vacuum solution.

SolarisOne and shlosmem
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Who said it has no mass?
I did
There is no mass anywhere in the manifold.

I did
I see. But if we interpret what you said as meaning that a white hole has no mass it also means that a black hole has no mass.

Your point, I think, is that the mass of a Schwarzschild black/white hole is a feature of the spacetime geometry, and not associated with any matter or radiation. I think that seems to have passed @shlosmem by.

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it also means that a black hole has no mass
Yes, since it is a vacuum solution there is no mass anywhere in the manifold. There is a characteristic length scale for the manifold, the Schwarzschild radius. In geometrized units mass has dimensions of length, so you can turn this length scale into a mass scale, but it is important to recognize that this mass isn’t in the Schwarzschild spacetime.

Of course, this is confusing since in a collapse spacetime there is mass and in the vacuum outside of the collapsing mass the characteristic mass/length scale of the curvature is equal to the mass of the collapsing matter. But as described earlier a white hole cannot be formed from collapse. So we are left only with the length scale.

Mentor
since it is a vacuum solution there is no mass anywhere in the manifold. There is a characteristic length scale for the manifold, the Schwarzschild radius
While I understand what you mean by this, it is non-standard terminology and will cause confusion (as, indeed, it already has in this thread).

I would rephrase it as: since the black hole is a vacuum solution the stress-energy tensor is zero everywhere in the manifold. There is a characteristic geometric parameter associated with the solution, which is usually referred to as "mass" but which is better understood geometrically as a characteristic length scale; however, it is called "mass" because from far away the black hole looks and behaves just like any other object with the same mass, and has the same gravitational effects.

shlosmem
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as described earlier a white hole cannot be formed from collapse. So we are left only with the length scale.
But the white hole still has the same attractive gravity as any other object with the same mass. The difference is that you can't actually fall into the white hole; you end up falling into the black hole region of the same global spacetime geometry instead.

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it is non-standard terminology and will cause confusion (as, indeed, it already has in this thread).
I disagree with your assessment. The confusion is caused by the standard terminology. Because the standard terminology calls the length scale a mass there is a reasonable but incorrect assumption that there is actually mass in the spacetime and that the mass is the cause of the gravitation. I am trying to clarify for the OP a point that is unclear precisely due to the standard terminology.

The white hole gravitates as a spherical object with a certain mass, but mass is not always the source of gravitation in GR and a white hole is one example of a scenario where there is gravitation without mass or even stress energy.

But the white hole still has the same attractive gravity as any other object with the same mass.
Yes, as the OP said
Black hole can have a satellite , it means that on time reversed e.g. white hole will have also that satellite

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The confusion is caused by the standard terminology. Because the standard terminology calls the length scale a mass there is a reasonable but incorrect assumption that there is actually mass in the spacetime and that the mass is the cause of the gravitation.
To me, the way to solve this confusion is to distinguish between "mass", a global geometric property, and "stress-energy", a local property. In any physically realistic spacetime, if there is mass (global property), there is stress-energy somewhere (local property). But there are physically unrealistic solutions of the Einstein Field Equations that have mass without having stress-energy, one of which is the maximally extended Schwarzschild spacetime that contains both a white hole and a black hole. There are no physically realistic spacetimes that contain white holes (for the reasons you gave earlier in the thread), which is why it is never possible to explain the mass of a white hole in terms of stress-energy somewhere.

This seems to me to be a better way to address the confusion because then we don't have to explain how a length scale can gravitate, which is the confusion that emerged earlier in this thread.

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To me, the way to solve this confusion is to distinguish between "mass", a global geometric property, and "stress-energy", a local property.

This seems to me to be a better way to address the confusion because then we don't have to explain how a length scale can gravitate, which is the confusion that emerged earlier in this thread.
Well, I don’t feel this is much of an improvement. You said “‘mass’, a global geometric property”. That begs the question: what kind of geometric property is “mass”? It is a length scale. So your explanation is the same as mine, but with sneaky terminology.

The only reason that we wouldn’t “have to explain how a length scale can gravitate” is because we snuck the length scale in by using the word “mass.” We are counting on the word to give a false impression in order to avoid discussing a challenging concept. I don’t think that is the way to go.

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The only reason that we wouldn’t “have to explain how a length scale can gravitate” is because we snuck the length scale in by using the word “mass.”
I would say we used the word "mass" because that's what we use for objects that can gravitate. But I agree that we still have to explain how that can correspond to a length scale, so we're stuck with that either way.

Dale
I think the confusion comes from using mass when it is meant matter. The space-time is vacuum so there is no matter in it(the stress-energy tensor is zero) but the space-time has mass.

shlosmem
Gravity is more complicated than it is in Newtonian theory. In GR, there are non-trivial vacuum solutions, including the maximally extended Schwarzschild solution. A vacuum solution is one that describes a way that gravity can exist without any source.

In other words, spacetime can simply curve this way even without mass. That is what it means for something to be a vacuum solution.
So when the white hole explode it means that we get material out of vacuum which brings new quotations.
1. What about the energy preservation law ?
2. As mentioned, black holes eventually disappearing dou to Hawking radiation, in other words the original mass that fails into the black hole find itself out as radiation energy. So in the reverse process this energy go in into the white hole and since energy is equivalents to mass, we must assume that the space geometric is not just a vacuum.

PeroK
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So when the white hole explode it means that we get material out of vacuum which brings new quotations.
1. What about the energy preservation law ?
2. As mentioned, black holes eventually disappearing dou to Hawking radiation, in other words the original mass that fails into the black hole find itself out as radiation energy. So in the reverse process this energy go in into the white hole and since energy is equivalents to mass, we must assume that the space geometric is not just a vacuum.
The maximally extended Schwarzschild solution is a hypothetical universe in which there is only a vacuum - by definition. It wasn't created by a collapsing star in our universe; it wasn't created by an explosion.

It's more mathematics, than physics. It's purely a solution to the Einstein Field Equations. There is no quantum mechanics (or any other physics to complicate things). It's a hypothetical model of spacetime and nothing else.

My advice is to treat the whole thing as mathematics, not physics. And whatever you do, find some way to comprehend that it is not and cannot be part of the universe we live in.

Dale and martinbn