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Spacetime topology

  1. Dec 18, 2008 #1
    Hey there,
    I'm looking for popular theories concerning the topology of space-time. Can anyone point me in the direction of a link? Or perhaps even just give me the name of a theory or two?
  2. jcsd
  3. Dec 18, 2008 #2
  4. Dec 18, 2008 #3


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    Lol, Imamura's lectures were posted 1995 before the observation of dark energy. In effect the lecture you link to contains serious misinformation which is likely to confuse people.

    You could try the Einstein-online link in my sig. It's fairly up-to-date.
    What do you have in mind specifically, when you say topology?
    Most of the topology issues are really simple---let me give you a sample:

    Is overall spatial curvature positive? (so space topology is so-called three-sphere S3, analogous to the 2D surface of an ordinary sphere, this is the space closed case and it does NOT imply eventual collapse)

    Or is overall spatial curvature zero? (this is the socalled flat case, it doesnt mean naive 2D flatness, it means conventional uncurved 3D space)

    Or is overall spatial curvature negative (angles of large triangles sum to less than 180, volume of ball increases faster than cube of radius, more galaxies at a given distance than you'd normally expect, because more volume, saddleshape picture used as illustration, not very likely)

    Current data of many sorts is a better fit to either flat case or slight positive curvature (closed) case. Negative curvature (sometimes called "open") is less favored, though still not ruled out.

    Is that sort of discussion what you had in mind? Or by topology do you mean fancier more fantastic cosmo models, like toroidal sometimes called "wraparound" or "PacMan"? There are a few cosmologists---a French guy Luminet comes to mind---who have spent time thinking up fancy wraparound topology models but they don't attract much attention. Three guys (Spergel, Cornish, Starkman) took the trouble to rule out these wraparound topology models, out to the limits of the observable universe---to show that they don't fit the data, there is no evidence for them at the scale of the observable universe. Basically other people ignore that kind of wraparound stuff. It is only interesting or fun as something to disprove. My guess is you are not primarily interested in the fancy topology speculation of Luminet etc. But if you are, would you like a link to the papers by Spergel, Cornish, Starkman politely disposing of it?

    Main thing to take away from discussion is that closed universe does NOT imply eventual collapse. It just means space has finite volume-----boundaryless and closed the way a ring or ordinary sphere is closed.

    Before 1998 there was the mistaken belief that this implied eventual collapse to a socalled big crunch :biggrin:. After 1998 that mistake was corrected. Closed case can continue expanding indefinitely just like flat case.

    Ask if you have more questions.
    Last edited by a moderator: Dec 18, 2008
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