Wick-rotated Riemannian metric that takes leaky gravity into account

[Onyx]

TL;DR

Wick-rotated riemannian metric that takes leaky gravity into account

This is pretty theoretical, so I don't know whether it would better belong in the "other physics" section. As I understand it, a pair of pants situation of topology change where one universe splits in two is described by a global wick-rotated riemannian metric so as to avoid the causality violations that would arise from a global lorentzian description. I think even if the metric is piecewise and/or discontinuous, that is okay, so long as it avoids CTCs. Now, philosophically speaking, what resides between the universes can be two things. In the purely intrinsic description, the question is without meaning. But the alternative is that it is the bulk between two branes. And this is where the question arises: the wick-rotation is done so that one brane branch is causally disconnected from the other, but of course we know that (at least in the brane theories I've heard) gravity can leak through. So I guess the question then becomes, how do we make a space that becomes two causally disconnected (geodesic and arbitrary curve wise) spaces but yet the local curvature in one brane can leak through the bulk to the other?

 

[PeterDonis]

As I understand it, a pair of pants situation of topology change where one universe splits in two is described by a global wick-rotated riemannian metric

the wick-rotation is done so that one brane branch is causally disconnected from the other, but of course we know that (at least in the brane theories I've heard) gravity can leak through

To have a meaningful discussion, we need some references, particularly for the statements quoted above. "As I understand it" and "I've heard" are not enough to give a valid basis for discussion. There are published papers discussing what you appear to want to ask about.

 

[Onyx]

Now, I could be mistaken, but I think this paper is suggesting that while topology change is a singular event in the brane-bound description, it smooths out when considering the overall bulk mathematically. It mentions self-intersecting branes as a means to allow topology change, which for me is hard to conceive of in the purely intrinsic view. But then it says that there can be signature change in the intrinsic braneworld view of a globally lorentzian bulk spacetime.

This paper isn't about a pair-of-pants scenario specifically, but it says that globally lorentzian treatments of topology change in general lead to singularities and CTCs.

This formed part of the inspiration for my question. You can see J. Richard Gott holding a menorah-like piece of blown glass representing a spacetime diagram where one trunk makes many branches (I'm paying less attention to the CTC at the bottom of the trunk). Now, if I were to use my own intuition for a second, I can't really conceive of a proper distance spatial boundary(s) that the curve would cross in order to get into one branch or the other. The other thing is that the fact that coordinate time apparently just terminates at the crotch suggests to me that more than just a classical treatment is needed.

But back to the sources, while I don't understand the first source entirely, I think I can say at this point that a metric that includes the extra dimension(s) explicitly is the most straightforward way to describe inter-brane leaky gravity, although what remains slightly unclear to me is whether a wick-rotation is still needed to enforce curve causal isolation or if a factor behind the bulk dimension can accomplish that.