Naked singularities and traversable wormholes

[FtlIsAwesome]

From what I know, for a wormhole to be traversable it must be held open by negative mass.
A naked singularity is a black hole whose spin is enough that it counteracts its own gravity and allows the singularity itself to be seen.

I had this thought: Could a wormhole composed of two naked singularities be an alternative to using negative mass?
Would this also eliminate tidal forces associated with wormholes that use negative mass?
Or would naked singularities require negative mass anyway to work as traversable wormholes?

 

[Nabeshin]

From what I know, for a wormhole to be traversable it must be held open by negative mass.

Well, I'd probably say that the negative energy density is required for it to be stable, but stability and traversability are closely related.

A naked singularity is a black hole whose spin is enough that it counteracts its own gravity and allows the singularity itself to be seen.

This is just one kind of naked singularity created by a maximally spinning hole. One can imagine naked singularities in other contexts.

I had this thought: Could a wormhole composed of two naked singularities be an alternative to using negative mass?
Would this also eliminate tidal forces associated with wormholes that use negative mass?
Or would naked singularities require negative mass anyway to work as traversable wormholes?

For one, traversable worm holes threaded with exotic matter need not have tidal forces at all. Secondly, for a wormhole to be traversable you'd rather not have singularities at all, since smashing into them makes the trip decidedly less pleasant! At any rate, the cosmic censorship conjecture has fairly widespread support, so I think people tend to shun away from naked singularities whenever possible.

 

[FtlIsAwesome]

This is just one kind of naked singularity created by a maximally spinning hole. One can imagine naked singularities in other contexts.

I didn't know that there are other types. What are they?

For one, traversable worm holes threaded with exotic matter need not have tidal forces at all.

Okay. I thought I read somewhere that a wormhole would need a mass, or size, more than Jupiter for tidal forces to not pull apart incoming objects. Can't remember where I read that. Maybe it was talking about black holes, not wormholes.

Secondly, for a wormhole to be traversable you'd rather not have singularities at all, since smashing into them makes the trip decidedly less pleasant!

Wormholes can work without singularities?

At any rate, the cosmic censorship conjecture has fairly widespread support, so I think people tend to shun away from naked singularities whenever possible.

Maybe they should rename them... horizonless singularity sounds a lot cooler.

 

[Nabeshin]

I didn't know that there are other types. What are they?

Well the first one that comes to my head is the charged black hole singularity, which has a similar maximal property to the rotating hole. But that's not really my point. My point is that a naked singularity is just some generic property of spacetime, and I don't think it's necessarily important to concern ourselves with how they are created (in this context!).

Okay. I thought I read somewhere that a wormhole would need a mass, or size, more than Jupiter for tidal forces to not pull apart incoming objects. Can't remember where I read that. Maybe it was talking about black holes, not wormholes.

Well it is certainly true that a black hole needs to be a certain size for a human not to be torn apart as they cross the event horizon (size is roughly supermassive black hole scale), but eventually they succumb to tidal forces obviously.

The issue of the actual tides during the travel through a traversable wormhole is a bit tricky. It is possible to construct a situation in which there is zero radial tides as you pass through the wormhole. In such a case, the tides are dependent on the speed with which you pass through the wormhole. In general, it is also true that the tides are inversely proportional to the size of the wormhole (to some power, depending on the specifics of the case). And since the amount of matter necessary to make the wormhole stable scales with the radius of the wormhole throat, I suppose you could say that one needs more mass to reduce tides, but only as a means to the end of stabilizing the larger throat. It does depend on the specific construction of the wormhole though. The "jupiter mass" figure that's thrown around is, I believe, an estimate of the amount of exotic matter necessary to keep a roughly human sized wormhole stable.

Wormholes can work without singularities?

Yes! We throw out models with singularities when restricting ourselves to traversable wormholes precisely because those with singularities will rip you apart!

 

[FtlIsAwesome]

How do wormholes without singularities work? Where can I read up on this?

I am also interested in the interior of wormholes. It is generally depicted as a tunnel. What happens when you try to travel to the edges of the tunnel (left-right-up-down sides, with the mouths front-back)? I don't think they are "solid walls". Is there a force that pushes objects to the center, or do the sides wrap around?

But back to my original question, can wormholes using naked singularities not require negative mass?

 

[FtlIsAwesome]

However in the pure Gauss-Bonnet theory (a modification to general relativity involving extra spatial dimensions which is sometimes studied in the context of brane cosmology) exotic matter is not needed in order for wormholes to exist- they can exist even with no matter.

This statement seems related to what you said about wormholes not needing singularities, but the page doesn't elaborate much further.

 

[HarryRool]

How do wormholes without singularities work? Where can I read up on this?

I'd recommend https://www.amazon.com/dp/0984150005/?tag=pfamazon01-20

Could a wormhole composed of two naked singularities be an alternative to using negative mass?

Here's what the Rodrigo book says about that:

"When the magnitude of the measure of the [rotating black hole] solution's angular momentum exceeds its mass..., the solution becomes a traversable wormhole... The Kerr [rotating black hole] solution... [h]as a gateway between our 'positive' universe and a 'negative' one. This negative universe possesses unusual features [including] a gravitationally repulsive [ring] singularity that appears to have negative mass... Travelers passing through this ring singularity are likely protected from lethal effects of radiation and tidal forces by the high value of the Kerr solution's angular momentum in this case." (p. 180).

I interpret this to mean that your intuition is correct. When there's a spin-induced naked singularity (angular momentum exceeds mass), you get a traversable wormhole with the ring singularity acting like a ring of negative matter through which travelers can pass.