# I Black holes with connected interiors?

Tags:
1. Dec 16, 2017

### stevendaryl

Staff Emeritus
I saw a video of a talk by Susskind discussing his ER = EPR idea. This post isn't actually about that talk, except that it got me thinking about wormholes. Without exotic means, I understand that it is basically impossible to have a traversible wormhole connecting two distant points in space. But something that is almost a traversible wormhole might be possible, and I'm wondering if it is a known solution of GR, or known to be impossible.

This almost-traversible wormhole would consist of two distant black holes with a connected interior. More specifically, I mean that there is a nonsingular point $e$ in the common interior of the two black holes, and two future-pointing timelike worldlines: $\mathcal{P}_1(s)$ and $\mathcal{P}_2(s)$ such that
• $\mathcal{P}_1(0)$ is in the exterior of the first black hole.
• $\mathcal{P}_2(0)$ is in the exterior of the second black hole.
• $\mathcal{P}_1(s_1) = \mathcal{P}_2(s_2) = e$ for some pair of proper times $s_1$ and $s_2$ (and the shared point is in the common interior of the two black holes).

In informal terms, is it possible for two people (say two lovers on the opposite sides of a galaxy) to each fall into their own black hole and meet in the interior (and enjoy a few moments together before being crushed by the singularity)?

The origin Einstein-Rosen bridge is I think similar to this, except for a couple of differences:
1. One of the ends is a white hole, rather than a black hole.
2. One of the worldlines is past-pointing, instead of future pointing (the one whose end is at the white hole describes something emerging from the white hole, rather than falling into it)
3. The common point $e$ is the singularity (not a good place for lovers to meet).

2. Dec 16, 2017

### Haelfix

It's actually possible to have a traversible wormhole in semiclassical gravity in AdS space. This requires having to violate the classical averaged null energy condition. This has been constructed explicitly here:

https://arxiv.org/abs/1608.05687

The required form of the coupling is essentially nonlocal. Note that, even classically you can make the wormhole *almost* traversible as they discuss in the lecture, if you start way on the far bottom right of your Penrose diagram and send a shockwave through. It almost touches the left exterior (but it just barely hits the singularity)

3. Dec 16, 2017

### PAllen

I believe your scenario is possible in pure classical GR, without need for violating even the dominant energy condition. As you say, it isn’t traversible. What is certainly true is that two such world lines are possible as infallers from the two exteriors of KS BH. I don’t see any obstacle to doing topological surgery to connect the two exteriors far from the BH. This would make it appear to be two widely separated BH.

4. Dec 16, 2017

### stevendaryl

Staff Emeritus
I think I'm confused---for the KS black hole, I thought that one end was a white hole. Both ends are black holes?

5. Dec 16, 2017

### PAllen

The KS spacetime has two exteriors that join in each interior region. By topological sewing you can connect the exteriors far from the interirors. Then the same BH will be acessible from two widely separated regions. It will appear to be two connected BH. Bob and Alice can fall into two different portions of the BH interior (-U direction, +U direction), meeting before hitting the singularity if the timing is right.

6. Dec 16, 2017

### Haelfix

You should be able to draw this and see it visually on a Penrose diagram. Start in region I on the bottom right hand side and have Alice send a 45 degree line into the interior. It will hit the singularity, but then you can arrange it for Bob to be positioned in region 3 so as to be able to intersect this line right before they both hit the singularity. They can then briefly compare notes, assuming the identification of the spacetime's has been made as Pallen mentioned.

7. Dec 19, 2017

### zonde

I have seen two dimensional pictures with KS chart (with x and t coordinates). But y and z are left out of this diagram. Aren't two exterior regions joined into one when we add say y coordinate and imagine three dimensional diagram?

8. Dec 19, 2017

### Staff: Mentor

No. A "point" on the K-S diagram represents a 2-sphere. The points in region I of the diagram (the right-hand exterior region) represent different 2-spheres than the points in region III of the diagram (the left-hand exterior region). They're not connected.