In what year was wormhole collapse discovered?

[mollwollfumble]

In what year was it first discovered that wormholes are non-traversable because the introduction of infalling matter caused the throat to collapse? Who discovered this?

 

[MathematicalPhysicist]

No one, since we don't even know if wormholes exist; in physics if you cannot do an experiment then everything could happen.

When will have experiments to check for wormholes in nature then we could prove or disprove this claim; it's also a possibiliy that some wormholes are relatively stable I mean upto some threshold mass.

 

[pervect]

Taking some liberties in interpreting the question, the first paper I know of that mentions that exotic matter is needed to hold open the throat of a wormhole is "Wormholes, Time Machines, and the Weak Energy Condtion" by Morris, Thorne, and Yurtsever. It's marked as "Received june 1988".

A snippet:

The Schwarzschild metric, with an appropriate choice of topology, describes such a wormhole. However, the Schwarzschild wormhole's horizon prevents two-way travel, nd its throat pinches off so quickly that it cannot be traversed in even one direction. To prevent pinchoff (singularites) and horizons, one must thread the throat with nonzero stress and energy.

They refer to another paper by Morris & Thorne, but list it as "to be published", on the last point.

It's possible there is some earlier paper than this that talks about the issue, though. This is the earliest one I know of.

 

[mollwollfumble]

Thanks Pervect, yes, I know about the Morris and Thorne work as the origin of the use of exotic matter to hold open the throat of a wormhole in 1988.

I'm sure that I read about the throat collapsing (in the absence of exotic matter) some time before the exotic matter variation came out. But when I now go looking in public records and technical papers about it, all I seem to be able to find is that it's either a well-known consequence of the black hole equations developed in the 1960s or links forwards to the 1988 paper. I'm sure that the collapse of the throat as soon as matter enters the black hole was not known in the 1960s or early 1970s, but that still leaves open a timespan of 15 or so years when this very important theoretical result could have been discovered.

I looked at the Morris and Thorne paper and it contains no reference back to the earlier work.

 

[mollwollfumble]

Looking into this a bit more. I'm starting to narrow in on the discovery timescale.

Let's start with the Kerr metric. This describes a rotating black hole, the singularity is in a ring about the centre and it was thought for a long time that travel through this ring would be survivable, and take travellers through to another universe or perhaps to a distant part of the same universe, a wormhole.
In 1971, Misner Thorne & Wheeler's book Gravitation had that view.
In 1975, Stewart in "On the stability of Kerr's space-time" tried to prove that the centre of a Kerr black hole was a stable environment, but couldn't rule out the possibility that it may be unstable.
In 1983, Detweiler in "Instability of some black holes" showed that the Kerr wormhole throat was unstable to some influences, but couldn't rule out stable travel through a wormhole.

So that limits the discovery of wormhole throat collapse to somwhere between 1983 and 1988. Unless it was already known in 1983 but unknown to Detweiler.

Possibly this paper from 1983? I don't have full access.
https://www.researchgate.net/publication/253740677_The_inner_horizon_in_the_Kerr-Newman_metric
It says something about small local perturbations at the event horizon generating infinite energy density at the inner Cauchy horizon. The gravity of matter falling through the event horizon would perturb it slightly, so can I take it that the infinite energy density suffices to destroy infalling matter before it can pass through the wormhole?

 

[PeterDonis]

that limits the discovery of wormhole throat collapse to somwhere between 1983 and 1988. Unless it was already known in 1983 but unknown to Detweiler.

It depends on what you mean by "wormhole throat collapse". There are quite a few complications involved in this issue.

The fact that the wormhole throat in the maximally extended Schwarzschild metric collapses too fast for anything to traverse it, even one-way, was known in the early 1960's, pretty much as soon as the maximally extended metric was worked out. (IIRC, MTW talks about this.)

The fact that the interior of the Schwarzschild metric is unstable against small perturbations (the kind that would be caused by any small amount of matter or radiation falling in) was known in the mid to late 1960's. (IIRC, MTW talks about this as well. Thorne's 1993 book Black Holes and Time Warps discusses this period in some detail. That book's bibliography is also an excellent source of references for this subject, including scientific papers.) I think the stability of the Reissner-Nordstrom and Kerr interiors was also investigated during this period (i.e., I don't think the 1975 Stewart paper was the first attempt to investigate this).

Btw, a key difference between Schwarzschild and the other two is that the other two have inner horizons as well as outer horizons; Schwarzschild only has one horizon, which is basically the analog of the outer horizon in the other two. So the stability of the interior involves effects at or near the inner horizon, which brings in issues that aren't present in the Schwarzschild case; a key one is the "infinite blueshift" of matter or radiation falling in, which most physicists believe indicates that the inner horizon won't actually exist--quantum gravity effects will come into play well before that point. But we don't have a good theory of quantum gravity so we can't say for sure.

Also, because of the inner horizons, the maximally extended Reissner-Nordstrom and Kerr geometries have a very different structure from the maximally extended Schwarzschild geometry; it's not even clear that the term "wormhole" is a good term for what's going on. The singularities are timelike, not spacelike, and in the spacetime beyond the ring singularity in the Kerr case (which has negative values of $r$ in the usual coordinates), the black hole appears to have negative mass. An observer who goes inside the inner horizon but avoids the ring singularity will eventually emerge into another Kerr interior and another external universe, but this universe is "in the future" of the original one and it's not clear how, if at all, it could be connected to the original one.

The Morris-Thorne-Yurtsever papers in the late 1980s were the first, AFAIK, to explicitly talk about possible travel through wormholes threaded by exotic matter; but the fact that exotic matter is required to hole a static wormhole throat open was known in the early 1970's. In Black Holes and Time Warps, Thorne tells about sending a draft of the wormhole paper to Don Page, who sent back a quick note pointing out that exotic matter being required to hold a static wormhole throat open was a direct consequence of a theorem proved in Hawking & Ellis (published in the early 1970s).

 

[MathematicalPhysicist]

What is this exotic matter? Have we detected its existence?

 

[PeterDonis]

What is this exotic matter?

It is matter that violates the weak energy condition. To an observer at rest in the throat of a hypothetical wormhole held open by exotic matter, the matter would appear to have a tension in the radial direction greater than its energy density.

Have we detected its existence?

No, and most physicists believe it cannot exist.

 

[mollwollfumble]

Although hardly known, this discovery has huge implications for science fiction. Nearly all black holes are Kerr black holes, because angular momentum is conserved, because nearly all large rotating objects are oblate, and because nearly all large objects are electrically neutral. (And because string theory relies on supersymmetry which has been ruled out by the LHC.)

If all Kerr black holes were traversable wormholes (traversable in the sense of letting small objects such as single atoms through) then the universe would be awash with traversable wormholes.

But this discovery shows that all natural wormholes are non-traversable. This discovery ought to be better known.

 

[mollwollfumble]

It is matter that violates the weak energy condition. To an observer at rest in the throat of a hypothetical wormhole held open by exotic matter, the matter would appear to have a tension in the radial direction greater than its energy density.
No, and most physicists believe it cannot exist.

You probably understand this better than I do.

My understanding was that exotic matter in this context has an inverse relationship between pressure and density. When you increase the pressure the density decreases and vice versa.

I thought exotic matter was possible in much the same way as negative refractive index is possible, through the use of metamaterials.

According to Wikipedia (the Wikipedia article is not well written), this type of exotic matter has negative mass, which has been suggested as a possible explanation for dark energy (phantom energy model). But so far phantom energy has been ruled out for dark energy by Occam's razor, because the cosmological constant model is both simpler and in better agreement with observation.

 

[PeterDonis]

this discovery has huge implications for science fiction

Off topic here. Sci fi can be discussed in General Discussion, but not in the technical forums.

(And because string theory relies on supersymmetry which has been ruled out by the LHC.)

What does this have to do with black holes?

this discovery shows that all natural wormholes are non-traversable

You're assuming that every Kerr black hole is a "natural wormhole". That is, as I have already pointed out, not a good way to think about Kerr black holes.

Also, I'm not sure which "discovery" you are talking about, since none of the discoveries discussed in this thread show that Kerr black holes are "natural wormholes" that just happen to be non-traversable. The discovery that exotic matter is needed to hold a wormhole throat open has nothing to do with Kerr black holes; it is based on a different spacetime geometry. The discovery that the interior of the Kerr spacetime is probably unstable against small perturbations does not mean that Kerr black holes are wormholes but are non-traversable instead of being traversable; it means they aren't wormholes at all, because the portions of the maximally extended geometry inside the inner horizon, and probably a good way outside the inner horizon, don't exist at all in real holes. (This is also true of the wormhole in the maximally extended Schwarzschild geometry; it doesn't exist at all in real holes.)

My understanding was that exotic matter in this context has an inverse relationship between pressure and density. When you increase the pressure the density decreases and vice versa.

I don't know where you got this from, but it's not correct. See my previous post.

According to Wikipedia

Wikipedia is not a valid source. Certainly not for something like this. Please, if you are really interested in this topic, take the time to read actual papers, such as the Morris/Thorne/Yurtsever papers referred to earlier in this thread.

this type of exotic matter has negative mass, which has been suggested as a possible explanation for dark energy (phantom energy model)

Phantom energy doesn't have "negative mass" in any ordinary sense; it just violates various energy conditions. The equation of state it obeys is of the sort that could theoretically hold a wormhole throat open; but, as you note, there is no evidence that it actually exists.

 

[Vanadium 50]

And because string theory relies on supersymmetry which has been ruled out by the LHC

Not true either.

 

[pervect]

A few things I think that should be mentioned:

1) Neither the Schwarzschild geometry nor the Kerr geometry represents the geometry of an actual collapsing black hole. So it's probably wrong to draw conclusions from either geometry about the actual nature of an actual black hole. In particular it's wrong to conclude from the fact that the Schwarzschild geometry is a non-traversible wormhole to conclude that the realistic collapse geometry must be similar to a wormhole. It's also wrong to conclude that because the Kerr metric has a timelike singularity, that the actual geometry due to a physical collapse must have a timelike singularity.

The ?good? news is that we do know from the singularity theorems that some sort of singularity does occur in standard GR, even if we can't say very much about it's nature with complete mathematical confidence.

It's hard to give an accurate but comprehensible description of why neither the Kerr nor Schwarzschild geometries represent realistic collapse, so I'll settle for one that is probably not accurate in detail but may convey some understanding of the difficulties. Both the Schwarzschild and Kerr geometries assyme perfect spherical symmetry. The problem is that in an actual collapse, the initial configuration of the matter won't be perfectly symmetrica as it is in the idealizations. The real issue is that these assymetries make a difference, because once the collapse process reaches a certain point, the asymmetries grow with time rather than shrink with time.

One issue specific to the Kerr geometry is to consider what happens if particles fall into (accrete) onto the geometry. It turns out these particles would gain infinite energy, destroying the geometry. So this geometry is unlikely to be physical.

2) If one happens to be a fan of wormholes, it's useful to know that there are some theories that are not GR, but an extension of GR (an extension that includes an effect known as torsion) which are likely to routinely produce wormholes.

But while wormholes are perhaps not "ruled out", they aren't necessarily an expected feature of the universe, either.

 

[MathematicalPhysicist]

A few things I think that should be mentioned:

1) Neither the Schwarzschild geometry nor the Kerr geometry represents the geometry of an actual collapsing black hole. So it's probably wrong to draw conclusions from either geometry about the actual nature of an actual black hole. In particular it's wrong to conclude from the fact that the Schwarzschild geometry is a non-traversible wormhole to conclude that the realistic collapse geometry must be similar to a wormhole. It's also wrong to conclude that because the Kerr metric has a timelike singularity, that the actual geometry due to a physical collapse must have a timelike singularity.

The ?good? news is that we do know from the singularity theorems that some sort of singularity does occur in standard GR, even if we can't say very much about it's nature with complete mathematical confidence.

It's hard to give an accurate but comprehensible description of why neither the Kerr nor Schwarzschild geometries represent realistic collapse, so I'll settle for one that is probably not accurate in detail but may convey some understanding of the difficulties. Both the Schwarzschild and Kerr geometries assyme perfect spherical symmetry. The problem is that in an actual collapse, the initial configuration of the matter won't be perfectly symmetrica as it is in the idealizations. The real issue is that these assymetries make a difference, because once the collapse process reaches a certain point, the asymmetries grow with time rather than shrink with time.

One issue specific to the Kerr geometry is to consider what happens if particles fall into (accrete) onto the geometry. It turns out these particles would gain infinite energy, destroying the geometry. So this geometry is unlikely to be physical.

2) If one happens to be a fan of wormholes, it's useful to know that there are some theories that are not GR, but an extension of GR (an extension that includes an effect known as torsion) which are likely to routinely produce wormholes.

But while wormholes are perhaps not "ruled out", they aren't necessarily an expected feature of the universe, either.

It would be terrific if wormholes can be stable, my gut feeling is that they do occur in nature.
But to devise such a device like stargate will need to advance on both Engineering and physics.

In what theories do wormholes get to be produced routinely?
And what does it mean routinely, you mean we should be filled with wormholes around us?

 

[PeterDonis]

Neither the Schwarzschild geometry nor the Kerr geometry represents the geometry of an actual collapsing black hole.

To be precise, neither of the maximally extended Schwarzschild nor Kerr geometries represents the geometry of an actual collapsing black hole. In the spherically symmetric case, the vacuum region exterior to the collapsing object is described by a portion of the Schwarzschild geometry. In the non-spherical case, we don't know that the vacuum region exterior to the collapsing object is exactly described by a portion of the Kerr geometry, but it is probable that the Kerr geometry does describe it to a good first approximation (as long as higher order moments of the object's mass distribution aren't too large--certainly once a rotating black hole is formed the Kerr geometry should describe its exterior).

Both the Schwarzschild and Kerr geometries assyme perfect spherical symmetry.

Not quite. The Schwarzschild geometry assumes perfect spherical symmetry, which basically means no property of the mass distribution other than the total mass itself is significant. The Kerr geometry assumes perfect axial symmetry, which basically means no property other than the mass and angular momentum is significant (i.e., no higher order moments).

The real issue is that these assymetries make a difference, because once the collapse process reaches a certain point, the asymmetries grow with time rather than shrink with time.

This is significant inside the (outer) horizon, but for objects of astrophysical size (stellar mass and larger) it is not expected to be significant at or outside the horizon. AFAIK the horizons of both the Schwarzschild and Kerr geometries (outer horizon in the Kerr case) are stable against small perturbations. It's only inside the horizon (well inside, for stellar mass and larger objects) that asymmetries start growing.

One issue specific to the Kerr geometry is to consider what happens if particles fall into (accrete) onto the geometry. It turns out these particles would gain infinite energy, destroying the geometry.

Again, to be precise, this happens at the inner horizon. So one way to avoid it is to assume that, as you noted, the interior of a real rotating hole is not the Kerr geometry far enough inside the outer horizon, because small asymmetries grow and cause the geometry to be something different, something that doesn't have an inner horizon and so doesn't give rise to the same issues. We don't know that this happens, but AFAIK it's certainly a possibility.

None of this changes what you (or I) have said about wormholes; but I think it's important to be precise about exactly what the Schwarzschild and Kerr geometries assume and what their limitations are. There is a lot of misinformation out there.

 

[GeorgeDishman]

This is significant inside the (outer) horizon, but for objects of astrophysical size (stellar mass and larger) it is not expected to be significant at or outside the horizon. AFAIK the horizons of both the Schwarzschild and Kerr geometries (outer horizon in the Kerr case) are stable against small perturbations

Presumably that is why the ringdown phase of the gravitational waves observed so far decays away even for a binary system progenitor.

 

[Cosmic Horseshoe]

To the best of my knowledge, the first paper to discuss the impossibility of traversal of a wormhole-like object (the maximally extended Schwarzschild solution) due to the rapidity with which its throat collapses is this one:

"Causality and Multiply Connected Space-Time" by Robert. W. Fuller and John A. Wheeler. Physical Review 128, No. 2 (15 Oct 1962): 919 – 929

It's mentioned in the The Physics of Stargates -- Parallel Universes, Time Travel and the Enigma of Wormhole Physics by Enrico Rodrigo (2010?).