Could someone point me in the direction of the relevant differential geometry/topology terminology/definitions/explanation etc. to express the idea that spacetime cannot be "torn".(adsbygoogle = window.adsbygoogle || []).push({});

Methinks it's "diffeomorphic invariance" but, even if it is, a few nice words and/or an example (or two...) of what's allowable and what isn't would be welcome.

And then, if it's not asking too much, how would I go about proving that two manifolds were inequivalent?

Specific example (based on spacetime surgery for creating wormholes):

1. Take a standard simply connected spacetime manifoldM

2. Consider the two situations

2a excise a pair of spheres (radius 1) centred at x_{1}= 1 and x_{2}= 10 and identify the surfaces of the two spheres.

2b ditto, but at x_{1}= 1 and x_{2}= 20

Being very specific that the x values are coordinate values and not distances (i.e. you can't expand/shrink the interval because the two x_{2}s are different points) , are 2a and 2b inter-convertible (if so, how etc.)?

I hope this is a sensible question...

Thanks, Julian

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# Spacetime - formal description of No Rip/Tear

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