Dragging a wormhole into a black hole

[CA Mason]

Assuming a wormhole exists, what would happen if one took one end of the wormhole into a black hole. Could they enter the wormhole and leave the black hole? What would be the result if they did?

 

[Chalnoth]

The way I understand it, wormholes can only exist if somehow the singularity that General Relativity says forms in the black hole doesn't actually form. My expectation would be that if one end of a wormhole fell into a black hole would be that because there is now a singularity, the wormhole connection would be destroyed.

That said, the singularity itself is a fiction. We may need to know the correct theory of quantum gravity to get the right answer. But my suspicion is that the real answer is just that wormholes are actually impossible.

 

[PeterDonis]

Assuming a wormhole exists, what would happen if one took one end of the wormhole into a black hole.

I don't think anyone has constructed a consistent solution of the Einstein Field Equation for this, so I think the answer as far as classical GR is concerned is "we don't know, because we don't know how to model it".

And since we don't have a theory of quantum gravity, I think the answer as far as quantum theory is concerned is the same.

 

[PeterDonis]

wormholes can only exist if somehow the singularity that General Relativity says forms in the black hole doesn't actually form.

It's a bit more complicated than that. The black hole spacetime geometry (more precisely, its maximal analytic extension) does have a "wormhole" in it, but it pinches off so quickly that nothing can traverse it: anything that tries to go through gets trapped inside the black hole and destroyed in the singularity.

A traversable wormhole requires "exotic matter" (more precisely, stress-energy that violates the weak energy condition) in order to hold it open: in this spacetime geometry, there is no event horizon and therefore no black hole at all (and no singularity); and the process of formation looks nothing at all like the formation of a black hole by gravitational collapse. So this geometry can't really be viewed as "what you would get if a black hole forms but somehow doesn't have a singularity at its center". The only common feature of the two geometries is spherical symmetry (in the idealized cases where we can construct analytical solutions).

My expectation would be that if one end of a wormhole fell into a black hole would be that because there is now a singularity, the wormhole connection would be destroyed.

As I noted in my previous post, to my knowledge nobody has constructed a solution of the EFE for this case, so we don't really know what the EFE predicts. The only wormhole geometries we have solutions for require the exterior of both ends of the wormhole to be asymptotically flat, which would not be the case if one end was inside a black hole. Also, as noted above, the wormhole spacetimes have exotic matter in them, whereas black holes are vacuum solutions, and the process of black hole formation and the creation of the singularity at the center requires ordinary matter that obeys the weak energy condition: if exotic matter is present, that condition is violated and the Hawking-Penrose singularity theorems do not apply. So I don't think we have a clear answer either way even on heuristic grounds.

(Btw, the fact that exotic matter violates the conditions of the singularity theorems leads to one hypothesis for how quantum effects might prevent singularity formation: various quantum fields have states which can be shown to lead to effective stress-energy tensors that look like exotic matter.)

 

[Chronos]

A white hole has an exit, a black hole does not. It seems their coexistence in the same spatial region is incompatible.

 

[PeterDonis]

A white hole has an exit

I assume you meant a wormhole has an exit?

 

[nikkkom]

Hmm, this example should be given to numerical relativity folks! :)

 

[newjerseyrunner]

The only thing I could think of to add to this is that GR forbids tearing or patching Spacetime. This implies that before and after the collision, the universe must be topologically equivalent. This means that the wormhole can not vanish.