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.(adsbygoogle = window.adsbygoogle || []).push({});

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 [itex]e[/itex] in the common interior of the two black holes, and two future-pointing timelike worldlines: [itex]\mathcal{P}_1(s)[/itex] and [itex]\mathcal{P}_2(s)[/itex] such that

- [itex]\mathcal{P}_1(0)[/itex] is in the exterior of the first black hole.
- [itex]\mathcal{P}_2(0)[/itex] is in the exterior of the second black hole.
- [itex]\mathcal{P}_1(s_1) = \mathcal{P}_2(s_2) = e[/itex] for some pair of proper times [itex]s_1[/itex] and [itex]s_2[/itex] (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:

- One of the ends is a white hole, rather than a black hole.
- 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)
- The common point [itex]e[/itex] is the singularity (not a good place for lovers to meet).

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# I Black holes with connected interiors?

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