What kind of topology change does this Lorentzian metric describe?

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Discussion Overview

The discussion revolves around the interpretation of a Lorentzian metric presented in a paper, specifically focusing on the nature of spatial topology changes it describes. Participants explore whether the metric indicates a transition from connectedness to disconnectedness over time and question the periodicity of time in this context.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions the specific type of topology change described by the Lorentzian metric, suggesting it may involve a transition from spatial connectedness to disconnectedness.
  • Another participant identifies a specific example of a wormhole topology, referencing Wheeler's work and suggesting a change from nothing to a wormhole structure represented as ##S^1\times S^2##.
  • There is a clarification regarding which example of the Lorentzian metric is being discussed, with some confusion about the identification of the first example.
  • A later reply proposes that time values ##t=0## and ##t=1## could represent the state before and after the formation of an ##S^3## wormhole, respectively.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specific nature of the topology change described by the Lorentzian metric, and multiple interpretations are presented without resolution.

Contextual Notes

There is ambiguity regarding the definitions of the examples being discussed, and the implications of the periodicity of time are not fully explored.

Onyx
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TL;DR
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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