Good online report about wormholes?

[Sauron]

Simply by curiosity.

I have readed a lot about worm holes indivulgative literature.

Now i would like to read a bit of serious math about them. A preliminar research have given me various articles, but none goes to deep or it assumes some previous familiarity.

It isn´t really something of primary importance for my interests, but hey, they are funny

 

[chronon]

There are really two parts to the mathematics of wormholes. Firstly there's the general relativity of how a wormhole could exist. Secondly there are the calculations of how physics could be consistent, given an idealized 'time machine' wormhole.

Several books have a chapter on wormholes e.g.

Black Holes, Wormholes and Time Machines - Jim Al-Kahili
The River of Time - Igor Novikov
Black holes and time warps - Kip Thorne

but none of these go deeply into the maths. For that you need

Lorentzian Wormholes- Matt Visser

As for online resources, well there's always my web page:

http://www.chronon.org/Applets/bouncer.html

Some original papers on the subject are available on Arxiv:

Time Machines the principle of self consistency as a consequence of the principle of minimal action: http://xxx.lanl.gov/abs/gr-qc/9506087

II The Cauchy problem for a self interacting relativistic particle:
http://xxx.lanl.gov/abs/gr-qc/9607063

You might also be interested in :
Almost 200 citations directly referring to time machines or time travel
http://www.math.siu.edu/kocik/tm/tm-all-ch.htm

 

[pervect]

Visser's book (the one Chronon mentioned) is the standard reference / bible on wormholes, if you want a full treatment with all the math.

 

[da615]

Sauron,

The mathematical treatment of wormholes needs a fairly extensive background in tensor analysis, Cartan forms and point-set topology. Even if you are familiar only with tensor analysis, you have access to quite a bit of the Mathematical literature on the topic.

Basically, you are looking at solutions of Einstein's Field equations, which tell you that matter and energy fields cause space-time to curve. These equations have geometric terms on one side and matter/energy field terms on the other side. So basically the equations tell you that the geometry of space-time is expressible in terms of matter/energy fields that give rise to the particular geometry.

Now these equations are highly non-linear. This means that in order to get exact solutions, you need to make an educated guess about the geometrical "distances" and the field quantities in terms of certain parameters and use the Field equations to patch them up in a plausible way.

In other words, you need to be familiar with how to use tensor analysis to express the metric ("distance") terms and the field quantities. You also need to know how these quantities transfer to different reference frames, especially when you consider travel through wormholes.

 

[da615]

Not strictly on topic, but these are some good intro. notes to GR.

http://pancake.uchicago.edu/~carroll/notes/

 

[James Jackson]

Didn't a recent talk Stephen Hawkin presented anul the idea of wormholes? I haven't followed it closely but I believe it was related to black hole entropy etc. I don't know if the paper's out yet...

 

[Sauron]

Math is not a problem.

It was simple that i didn´t find a good expositioin of the ideas.

I have readed a very brief mentio on the book of Feyman "lecture notes in relativiy" which has clarified me the concept (curiously without using too much math).

Of course still i would like learn more. NOw that i have found the way to bypass the blocking of my ip to arxiv i will read the articles you have cited.

 

[pianoplayer]

An excellent introduction can be found in the paper by Morris and Thorne entitled "Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity," in the American Journal of Physics 56, 395-412 (1988).