Graduate What kind of topology change does this Lorentzian metric describe?

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The discussion centers on the interpretation of a Lorentzian metric presented in a paper, specifically regarding its implications for spatial topology changes. Participants debate whether the metric describes a transition from connectedness to disconnectedness over time and question the unusual periodicity of time (t). Clarification is sought on which example of the metric is being referenced, with confusion arising over the identification of the first example. Ultimately, it is suggested that t=0 signifies a state of nothingness, while t=1 indicates the formation of an S^3 wormhole. The conversation highlights the complexities of understanding topology changes in the context of Lorentzian metrics.
Onyx
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What kind of topology change does this Lorentzian metric describe?
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 paper specifying what kind. Also, why is ##t## periodic? That seems very unusual to me.
 
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Which one do you call the first example? The one that says that it is Wheeler's beloved wormhole? Then it describes the change from nothing to a wormhole ##S^1\times S^2##.
 
No, when I say the first example, I mean number 7, the Lorentzian metric with the off-diagonal entries.
 
Onyx said:
No, when I say the first example, I mean number 7, the Lorentzian metric with the off-diagonal entries.
That is the same example!
 
martinbn said:
That is the same example!
Oh, my bad.
 
Onyx said:
Oh, my bad.
Well then I suppose ##t=0## represents nothing and ##t=1## represents the ##S^3## wormhole having formed.
 

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