Good question JesseM
My first thought was: yes, I think I am saying that in classical relativity I thought the topology should be constant on each spacelike hypersurface from minus to plus timelike infinity. In which case, part of the question is "what's the proper way of describing such...
Thanks atyy -
I have the Sean Carroll (the information in quote you gave has, I think, ended up in the Wikipedia article on Diffeomorphism), and have just looked at the (scary) d'Inverno stuff. The Olver (where I could see bits) is obviously relevant too... so they are all, I suppose...
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".
Methinks it's "diffeomorphic invariance" but, even if it is, a few nice words and/or an example (or two...) of...
I thought it was worth looking for these but after employing the "usual techniques" was unable to find them freely available.
I did however recall on seeing Muller's home page that I have a another paper by him. For anyone who is interested, this one is freely available.
"How computers can...
You beat me to it: I had also looked again at the metric and for constant theta, l=0, phi seemed to cancel out the dt... suggesting precisely what I had "intuited" (an unreliable source at the best of times) but I was hesitant - unpacking old calculus etc. one wonders whether what seemed...
Two points about the spacelike nature of the embedding diagram... My hardcopy of Visser is in storage in England - I'm in Budapest - but the cover can be seen at Matt Visser's pages http://homepages.ecs.vuw.ac.nz/~visser/book.shtml"
1. Agreed, it is a view at an instant - but if the wormhole...
You mean light would not circle around the wormhole at its narrowest point? Ah. I must confess I have great difficulty visualising wormholes so intuition has led me very astray - can you help me to understand why? (apart from the embedding diagram limitations).
Second point though - if a...
Just for info... at the Living Reviews in Relativity article on Conformal Infinity http://relativity.livingreviews.org/open?pubNo=lrr-2004-1&page=articlesu3.html" , esp the point about 1 screen down where it says
Hmmm... I do tend to have a "shoot first, ask questions later approach." This would be so much easier at a whiteboard where as soon as I open my mouth you could tell me I've put my foot in it. (NB - I can't work out to "multiquote" properly)
To be honest, I was saying that 11.66 and 11.67 are...
No... I retract... sort of.
I think I now understand why Visser et al say - by application of the ADM Mass definition - that wormhole mouths acquire/lose mass as mass passes through the wormhole.
However, attending carefully to the definition of asymptotic flatness in terms of null lines...
George - thanks for making me think about the right things.
Having posted a short while ago, on the way home I suddenly thought, "I've answered my own question...!"
That having been said (I'll think it through more carefully and post longer later) I have to disagree with the statement that...
Aha. A search for the definition of asymptotic flatness turned up something useful in General Relativity by Malcolm Ludvigsen (http://books.google.co.uk/books?id=YA8rxOn9H1sC&lpg=PA115&ots=EZNOQ_U-kK&dq=define%20%22Asymptotic%20flatness%22&pg=PA115", see also attached quote JPG; copyrighted...
Um. Not sure about that bit, however, the equivalence principle - that in any sufficiently small reason a gravitational field is indistinguishable from acceleration - is pretty fundamental.
Here, the "sufficiently small region" takes care of eliminating the tidal forces that would allow you...