Recent content by 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...

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...

Okay, I think I figured out through pullback the form of h(x,y), the embedding function, is. It involves an indefinite integral whose answer is probably expressed with elliptic integrals in a way that I don't know. Maybe that question would be more at home in the pure math section of the website...

Yes, those are supposed to be the degenerate horizons of the black holes I think. I got this metric from a 2 black holed Majumdar-Papapetrou metric with black holes centered at the points you mentioned. I took the ##\phi=constant## slice and replaced what is usually ##p## and ##z## with ##x##...

Actually, forget about the Weyl metric for now. I am specifically trying to embed ##ds^2=U^2(dx^2+dy^2)##, where ##U=1+\frac{1}{\sqrt{(x-1)^2+y^2}}+\frac{1}{\sqrt{(x+1)^2+y^2}}##, into 3D Euclidean space. The only trouble is, the resulting function clearly does not have an indefinite integral...

Has anyone seen this question?

Is it possible to make an embedding of the ##\phi##=constant slice of a Weyl metric in ##R^3##? In particular, I'm thinking of a metric where the components are both ##\rho## and ##z## dependent.

Well then I suppose ##t=0## represents nothing and ##t=1## represents the ##S^3## wormhole having formed.

Oh, my bad.

No, when I say the first example, I mean number 7, the Lorentzian metric with the off-diagonal entries.

Well then I suppose for ##S^1 x S^2## it would be ##d\theta^2+d\psi^2+sin^2\theta d\phi^2##.

Looking at this paper, what sort of spatial topology change does the lorentzian metric (the first one presented) describe? Does it describe the transition from spatial connectedness to disconnectedness with time? All I know is that there is some topology change involved, but I don’t see the...

##dx^2+dy^2## or ##dr^2+r^2d\theta^2##.

How do I take the product metric of the circle and sphere metrics?

How do I find the metric tensor on ##S^1## x ##S^2##?