Singularity Theorem Proof on IanBay's Site

[julian]

At

http://members.lycos.co.uk/ianbay/

I'm attempting to write up the proof of the singularity theorem, but its not uite finished for various reasons...

In The large scales structure of spacetime on page 98 the following statement is made

"Further if any component of $\left( dA_{\alpha \beta}/ds \right) |_p$ is very large, the corresponding point on $\gamma \left(s\right)$ will lie near p, since in the limit the term $R_{\alpha 4 \gamma 4}$ in (4.39) becomes irrelevant and the solution resembles the flat space case."

This isn't immediatley obviuous to me, I wonder if anyone could help me out?

thanks

 

[marcus]

I'm not offering help with your proof, just saying hello and welcome. We have LaTex and the tags are [tax] and [/tax] but replace the a by e, so it is tex and /tex.
applying that to what you have in quotes

"Further if any component of

$$(d_{\alpha \beta}$$

is very large, the corresponding point on $$\gamma (s)$$ will lie near p, since in the limit the term

$$R_{\alpha 4 \gamma 4}$$

in (4.39) becomes irrelevant and the solution resembles the flat space case."

 

[julian]

hello marcus


I'm a docotr in theoretical condensed matter physics who wants to move into gravity. Gravity has always been a hobby of mine, but I don't know many people who do gravity and so thanks for your welcome - I hope to have many conversations with you type of people

ian

 

[julian]

hello marcus

thanks for the reference to "Lightness of Being: Mass, Ether, and the Unification of Forces". I haven't heard of this book it sounds very interseting.


sorry for my comment "you type of people" - people learn that I don't mean anything by these kind of comments - it's just my sense of humour

ian

 

[marcus]

Ian, there are several others around here who could be more helpful to you. I am a retired mathematician who loves to watch physics from the sidelines, the way science journalists and kibbitzers do. Have you tried posting questions in the General Relativity forum?

I'm curious about your choice of a research direction. I hope you have tenure or an otherwise secure position as a condensed matter physicist, that will serve as support while you venture into gravity. (Excessive curiosity is a major character flaw with me. You are welcome to ignore it.)

In case you are interested in conferences, we could share information. I think that the most important gravity professional society is the GRG (general relativity and gravitation) and they have the big international GRG conference every three years. It was held in 2007 in Sydney and will be held again in 2010 in Mexico City. You can find out the list of plenary talks, indicating the hot research topics and the leading people, by googling "GR18" or "GR 18 Sydney"

I'm curious about what line of gravity research you envisage going into. Gravity waves? Quantum gravity? Quantum cosmology? Classical cosmology? The search for signs of dark matter and dark energy and the attempts to learn about them?

there is also the Marcel Grossmann series of meetings on GR and gravity. the next MG conference is in Paris next year. they also run on a three year cycle. the 2006 MG 11 was in Berlin. But to me the MG organizers seem to have more limited vision and the MG lineup is never so interesting. Even though it is a year farther off, I am more interested in seeing the program for GR19 (2010) than I am in whatever will be talked about at next year's MG12. But maybe that one is more your cup of tea. Here is a link
http://www.icra.it/MG/

If you tell me what line of gravity or cosmology you envisage getting into I will try to think of interesting papers, recorded lectures, conferences.

Oh here is one, just at random, since you are interested in singularities. Have you watched the online videos of the workshop on Quantum Spacetime Singularities at the Santa Barbara Kavli (KITP). The workshop took place early in 2007. Gary Horowitz and Martin Bojowald were two of the organizers. There was a lot of discussion of how various approaches get rid of singularities (cosmological and black hole mainly). Bojowald and Ashtekar and Pullin were there for Loop cosmology, and there were a lot of String folks, and also some people who just do Classical GR.
I think if you google "KITP singularities" you will get it.

Maybe you were already well-aware of all the stuff I mentioned. Let me know it it was all old news to you---then I will know I have to work harder

 

[George Jones]

This isn't immediatley obviuous to me, I wonder if anyone could help me out?

I haven't had time to look at this. Have you looked at the same proof in Wald?

 

[julian]

Hi Marcus


Thanks for your advice. As I think you can tell from my report my interests are quite broad (thogh not expert)

I haven't researched the subject I would like to move into but what I find interesting is the problem of the establishing the true observables of classical GR and the resulting physical implications. If you could point me in the right direction that would be great.

thanks ian

p.s. If you or other people would like to contribute to my physics glossary, provide worked exapmples in general or critical remarks these would be gratefully appreciated.


Hi George


Yep, iv'e read p226-227 of Wald and I get the idea but I'd like to provide a more detailed explaintion myself.

It's been my experience that other sources refer to the same page of H and E!

In Wald p.g. 227 he states "... The full proof of this result can be found in proposition 4.4.2 of Hawking and Ellis.."

thanks

ian

 

[julian]

In Ray D'Inverno's book "Introducing Einstein's realativity" he says

"I think it would be generally excepted in the relativity community that the most authoritative text in existence in the field is the large scale structure ofspace-time by S. Hawking and George Ellis(pubed by Cambd press)" Indeed, this has taken on something akin to the status of the bible in the field..."

Since reading this book it has always been my ambition to write an excessible and comprehensice account - I've tried achieving this - trying to take out the slog of this - but not quite finished but if anyone is mad enough to help out that would be great

ian

 

[Chronos]

The most confounding aspect of gravity [to me] is it does not behave like your run of the mill field theory. GR suggests a gravitational field should induce its own gravity. This is an illogical result [infinite feedback], but, no one has adequately explained it.

 

[julian]

You should consider the

Newton–Raphson method, to find the roots of polynomial equations!


It's a method for finding successively better approximations to the zeros of a non-linear equation - the end result of an infite number of approximations is a finite number though!


Gravity is similar - you start with an aprroximation (a field over spacetime) which influences the next degree of approximation - it takes an infinite number of itereations to get to the exact answer but that does not imply the exact answer is infinity - just as the root of some polynomial equation isn't infinite!

ian

 

[julian]

Yes in finding the solution to a polynomial equation takes infinite feedback but that does not mean the end result is infinity - just as the root of a polynomial isn't infinite

 

[julian]

p.s. by the way, robert wald has shown that when the quantum mechanics of matter is taken in account - effectively the self-consistent equations of QGR lead to unstable, runnaway solutions which can only be accouncted for by LQG intervention


ian