Black Holes & White Holes: Same or Different?

[Gaussian97]

TL;DR Summary

Are Schwarzschild black holes and Schwarzschild white holes the same astronomical object?

Well, my question arises because when one hears about black and white holes in divulgation, usually one hears that they are two kinds of "objects", the first one is a region that can only absorb things, and nothing can escape from it. While the latter is a region that only emits things and nothing can enter it.
Also when one studies the Schwarzschild solution one finds that for $r<r_g$ one can find that the solution predicts either a black hole or a white hole.
Now my question is, are these two objects the same? Or two different objects? If the usual picture of black/white holes as two completely different things one may see the Schwarzschild solution as having two possibilities, either it produces a BH or it produces a WH. But I don't see anything to "determine" which solution you are dealing with, Schwarzschild solution is one and only one, and therefore it seems to me that both, BH and WH should coexist in the same space-time region.

So technically, if we could see a region described by Schwarzschild metric, we would see an object that is not a black-hole in the sense that we would see light (and possibly matter) coming out of it, but at the same time, anything that falls inside it wouldn't be able to escape from it. Is this right? Or I'm missing something?

 

[Ibix]

In the maximally extended Schwarzschild spacetime there is a black hole region and a white hole region. They are simply time-reversed copies of each other. Are they different things? Dunno. Depends how you are defining "thing", I guess. The event horizon of one, extended back in time, is the event horizon of the other.

However, the Schwarzschild black hole is eternal. It doesn't form from anything. It always has been and always will be, and you can see the white hole and its singularity as an artifact of that. If you use a realistic(ish) collapse model then there's no white hole and no second exterior region. Past and future are distinguishable because one contains a star and the other a black hole.

As with many physical models you can, in principle, run it backwards and describe a white hole exploding and turning into a star. That doesn't seem to be the universe we live in, however.

 

[Gaussian97]

Well, I know that in reality, Schwarzschild metric is kind of an idealisation since it's eternal and I assume no eternal solution can be "real" in a non-eternal universe, and also that it seems to be widely extended the idea that white holes cannot exist in our universe (I don't know if there is any theorem stating that).

When you say that in a realistic case you would have a star collapsing into a black hole or a white hole exploding to a star, it seems to fit this conception that they are two irreconcilable things.

When I ask if they are the same "thing" I mean that, if we could observe a the Schwarzschild solution we wouldn't observe either a black hole or a white hole, but both at the same time, i.e., both the BH and the WH coexist at the same time and same spatial location (as an exterior observer point of view).
So an observer would see "something" that is a BH in the sense that nothing that enters can escape, but it's not a BH because we would see light and matter coming out of it.

 

[Ibix]

When I ask if they are the same "thing" I mean that, if we could observe a the Schwarzschild solution we wouldn't observe either a black hole or a white hole, but both at the same time, i.e., both the BH and the WH coexist at the same time and same spatial location (as an exterior observer point of view).

Well, it depends what you mean by 'at the same time', then. Certainly light from inside the white hole interior can reach you wherever and whenever you are in either exterior regionn so if you look down, light coming up at you could be coming from the white hole. At the same time you could be firing test particles in orbits around the black hole.

I think that the coordinate independent statements you can make are:

• If you are in the exterior, some of the white hole is in your causal past and none of it is in your causal future. Some of it is spacelike separated from you.
• If you are in the exterior, some of the black hole is in your causal future and none of it is in your causal past. Some of it is spacelike separated from you.
• All events in the white hole region are in the causal past of all events inside the black hole.

Particularly in light of that last point, I think it's difficult to claim that the black hole and white hole co-exist. I think you can always pick a notion of "now" (a plane of equal Kruskal-Szekeres $v$ for some Kruskal-Szekeres coordinate system) such that the white hole exists "now" for any event in the exterior. Likewise, you can pick a notion of "now" such that the black hole exists "now". I don't think you can have both at once without some of your "now" lying in the causal future of other parts of "now", which doesn't seem like "now", really.

 

[Ibix]

The spatial location is the same, though, at least in the sense that if you build a spherical shell so that nothing can fall into the black hole without breaching it then nothing from the white hole can get out without crossing the shell either.

 

[PeterDonis]

my question is, are these two objects the same? Or two different objects?

They're two different objects. Even in the maximally extended Schwarzschild spacetime, where the white hole and the black hole are both part of the same spacetime geometry, they are two different, disjoint regions of that geometry.

 

[PeterDonis]

I don't think you can have both at once without some of your "now" lying in the causal future of other parts of "now", which doesn't seem like "now", really.

More precisely, it is impossible to find a single spacelike hypersurface ("spacelike hypersurface" is the best precise technical term we have that corresponds to our intuitive notion of "now") in maximally extended Schwarzschild spacetime that contains events in both the white hole and the black hole regions.

 

[Ibix]

("spacelike hypersurface" is the best precise technical term we have that corresponds to our intuitive notion of "now")

I was avoiding "spacelike hypersurface" in light of this recent discussion (post #8 et seq) about everywhere spacelike surfaces that have timelike separated events in them, so don't match a reasonable notion of "now". Not sure if that was a good idea or not...

 

[PeterDonis]

I was avoiding "spacelike hypersurface" in light of this recent discussion (post #8 et seq) about everywhere spacelike surfaces that have timelike separated events in them, so don't match a reasonable notion of "now".

Yes, that's a fair point.

A stronger term would be "achronal"--no two points in the surface can be connected by a timelike curve--and an even stronger term would be "acausal"--no two points in the surface can be connected by a causal (timelike or null) curve. The latter is the kind of surface we are looking for in this case; no acausal surface in maximally extended Schwarzschild spacetime can contain events in both the white hole and black hole regions.

 

[Gaussian97]

Yes, ok, sorry for my vague concepts, I think I understand what you mean. But what I want to say is that any observer with $r>r_g$ will see a black hole but also, at any time, can see that radiation came out of it, so any observer sees that the black hole exists but simultaneously is receiving light from the white hole.

I don't know if now it's more clear.

 

[dsaun777]

In the maximally extended Schwarzschild spacetime there is a black hole region and a white hole region. They are simply time-reversed copies of each other. Are they different things? Dunno. Depends how you are defining "thing", I guess. The event horizon of one, extended back in time, is the event horizon of the other.

However, the Schwarzschild black hole is eternal. It doesn't form from anything. It always has been and always will be, and you can see the white hole and its singularity as an artifact of that. If you use a realistic(ish) collapse model then there's no white hole and no second exterior region. Past and future are distinguishable because one contains a star and the other a black hole.

As with many physical models you can, in principle, run it backwards and describe a white hole exploding and turning into a star. That doesn't seem to be the universe we live in, however.

Are there any serious cosmological models that posit that the universe is just a massive white hole connected to a black hole?

 

[Ibix]

Yes, ok, sorry for my vague concepts, I think I understand what you mean. But what I want to say is that any observer with $r>r_g$ will see a black hole but also, at any time, can see that radiation came out of it, so any observer sees that the black hole exists but simultaneously is receiving light from the white hole.

I think the basic problem is that you are trying to put into normal words something that doesn't really fit.

Anywhere I am in spacetime it is possible for some part of the white hole interior to send me signals. So I can see, but never enter, the white hole. The converse is true of the black hole. I can never see it but I can enter it and send signals into some part of its interior from anywhere in spacetime.

If I'm inside the white hole, the black hole is unambiguously in the future - I cannot construct an acausal plane (a "now") that passes through me and the black hole. Likewise, if I'm in the black hole, the white hole is unambiguously in the past. But outside either, there is no unambiguous answer. I can construct acausal planes that pass through either the white hole or the black hole but not both, and I can make either of these constructions at any event in either exterior region.

Combining those paragraphs, outside the holes I am free to say "the black hole exists and the white hole doesn't any more", or "the white hole exists and the black hole doesn't yet", and I may switch at will between those claims. Either way, I can always say "I can see the white hole but cannot enter it, and I can enter the black hole but I cannot see it". I think this is slightly different from what you were saying.

 

[Ibix]

Are there any serious cosmological models that posit that the universe is just a massive white hole connected to a black hole?

No. The FLRW solution doesn't look anything like a black hole solution. Especially not like the maximally extended Schwarzschild solution which must be vacuum everywhere.

There do seem to be more exotic models that treat our universe as embedded in a higher dimensional structure and have it emerge from some kind of stellar collapse in that higher space. I don't know much about it (I just read the abstract of a paper the last time someone asked this and countered my "no" with "but I've read that..."), but I think that's somewhat beyond the scope of the relativity forum.

 

[dsaun777]

No. The FLRW solution doesn't look anything like a black hole solution. Especially not like the maximally extended Schwarzschild solution which must be vacuum everywhere.

There do seem to be more exotic models that treat our universe as embedded in a higher dimensional structure and have it emerge from some kind of stellar collapse in that higher space. I don't know much about it (I just read the abstract of a paper the last time someone asked this and countered my "no" with "but I've read that..."), but I think that's somewhat beyond the scope of the relativity forum.

Do you remember the paper?

 

[Ibix]

Do you remember the paper?

https://www.nature.com/news/did-a-hyper-black-hole-spawn-the-universe-1.13743

Proper references at the bottom of the article.

 

[Gaussian97]

I think the basic problem is that you are trying to put into normal words something that doesn't really fit.

Anywhere I am in spacetime it is possible for some part of the white hole interior to send me signals. So I can see, but never enter, the white hole. The converse is true of the black hole. I can never see it but I can enter it and send signals into some part of its interior from anywhere in spacetime.

If I'm inside the white hole, the black hole is unambiguously in the future - I cannot construct an acausal plane (a "now") that passes through me and the black hole. Likewise, if I'm in the black hole, the white hole is unambiguously in the past. But outside either, there is no unambiguous answer. I can construct acausal planes that pass through either the white hole or the black hole but not both, and I can make either of these constructions at any event in either exterior region.

Combining those paragraphs, outside the holes I am free to say "the black hole exists and the white hole doesn't any more", or "the white hole exists and the black hole doesn't yet", and I may switch at will between those claims. Either way, I can always say "I can see the white hole but cannot enter it, and I can enter the black hole but I cannot see it". I think this is slightly different from what you were saying.

Ok then my question should be if we can see both, the BH and the WH simultaneously, and the answer is yes, right? Thank you very much

 

[Ibix]

No, because you can't see the black hole from outside it. Only if you are inside the black hole can you receive signals from parts of all four regions.

 

[PeroK]

No, because you can't see the black hole from outside it. Only if you are inside the black hole can you receive signals from parts of all four regions.

We know the black hole is there, but we can't see it. We don't know the white hole is there, but we may be able to see it. Is that about it?

PS Hypothetically at least.

 

[Gaussian97]

Well, we should be able to "see" the black hole in the same way we can "see" black holes in our universe, of course, we cannot "see" their interior, but we know that the black hole is there, no?

 

[vanhees71]

Well, my astro colleagues have seen a BH (or rather what's to be expected to be seen of them) recently:

https://blackholecam.org/

 

[Ibix]

The problem with a maximally extended Schwarzschild spacetime is its extreme symmetry. It never changes. So there can't be a time "before the black hole" because that would imply a change to "after the black hole began to exist" (edit: or at least, not before it any more). You can apply an arbitrary division (those acausal surfaces), but you must be able to do that at any time because any time is exactly like any other.

That isn't the case with a realistic black hole. There is a region of spacetime where the stellar collapse event is in the future light cone, although this event never enters your past lightcone unless you dive into the hole. So there's meaning to "the black hole doesn't exist yet", even if it never becomes (strictly speaking) unambiguously true that it already exists.