Talk:Pp-wave spacetime

Major Rewrite
I have corrected the metric given in terms of the Brinkmann coordinates to include only the vacuum metrics. In the form previously given, we would allow either nongravitational radiation, or gravitational radiation, or both. In other words, we would have a null dust solution, not a vacuum solution! The term "gravitational wave" implies (at least to my mind) a vacuum pp-wave, in which there is no nongravitational massless radiation (in particular, no electromagnetic radiation) accompanying the gravitational radiation.

It is unfortunately true that "*-metric" is a standard term in the literature, but a metric tensor is a tensor field on a spacetime, not the spacetime itself. Since it is so easy to use less confusing terminology, why not do so? I would prefer to replace "pp-wave metrics" with "pp-waves" or "pp-wave spacetimes", but haven't done that, principally because I don't (yet) know how. --Hillman

Feedback on the Rewrite

 * When I created this page (139.133.7.38 was me), I intended using the term 'generalised pp-wave spacetimes' (I have a reference for that, which I'll include soon) to include nongravitational radiation as well as gravitational radiation. I agree that the term(s) 'gravitational radiation/wave' should be used exclusively for the vacuum pp-waves. I'll try and sort it out whilst keeping what is presently here.  Mpatel 08:21, 12 Jun 2005 (UTC)


 * Ok, I've renamed the page to 'pp-wave spacetimes'. To rename a page, click on move (at the top of the page) and follow the instructions. --- Mpatel 08:50, 12 Jun 2005 (UTC)


 * I hope the edits I've made are ok. I've included some general definitions (with a reference and an external link). Included the expression for the Ricci tensor to clarify why pp-waves with a 'harmonic H' are called vacuum pp-waves. --- Mpatel 09:52, 12 Jun 2005 (UTC)

Even More Major Rewrite
Hi, MP, thanks for the help, but I think you missed something Steele says: the "generalised" pp-waves are actually a special case! Yes, the terminology is appalling, and it gets worse as we have already seen. One of my major goals in my two rewrites has been to clarify the terminological confusion, but I think you inadvertently made things worse!

A few years ago, I set out to write a review paper for GRG on pp waves. That was fun, but I quit writing when the review reached 150 pages with several hundred citations. I just reviewed my draft for the first time in several years, and used parts of it as the basis for my second and far more extensive rewrite. This isn't perfect yet ;-/ but I've spent a lot of time on it, so please let it sit for a few days while I massage it a bit.

Anticipate these changes: a parallel rewrite of the article on plane waves, figures illustrating some of the geometric observations of Penrose and a diagram of the symmetry classification of pp waves (from my unpublished review).

About that review--- clearly the original review desperately needs to be broken down into various separate papers. Perhaps this pp wave wikiproject will help me do that.
 * --Chris Hillman

P.S.: Forgot to say something about citations: as I said, my review had hundreds, and obviously we don't want to repeat them all here. (Hopefully I will eventually be able to add a citation to some review of pp waves, either by myself or by someone else.) One thing that concerns me is that from my work on the review, I think there are some other papers which are more interesting/important in the long run than some which are currently cited, but I hesitate to start adding everything I think is at least as important as anything already there.

To keep things under control, I propose to limit the citations to a handful of really classic papers, plus some of the most relevant books. This might mean removing the citation to the paper by Steele, and maybe to the paper by Sippel and Goenner. These are interesting, but most readers will probably not find symmetry classifications as interesting as we do.
 * --Chris Hillman


 * Oops, I must've missed that statement by Steele that gen. pp-waves are a special case ! You've certainly included a lot about pp-waves that I wasn't aware of; I have no objection to leaving the article alone for a while. Just in case you're interested, I recently created a page on spacetime symmetries, so perhaps some of the classification work on symmetries could be included in there (warning: that page has no real content at the moment). --- Mpatel 09:20, 13 Jun 2005 (UTC)

Third Rewrite
As requested, I rewrote the nontechnical introduction to better help readers without a background in mathematical physics (and optimistically removed the "too-technical" flag). I also added some important information about SG11 plane waves, which I plan to expand on somewhat in future articles on Penrose limits and plane waves. I gotta do something else for an hour, but plan to write the plane wave article later today.

MP, thanks for the symmetry page! I plan to use this to seque into future articles on Weyl vacuumns, Ernst vacuums, Beck vacuums, Ehlers vacuums, and colliding plane waves, which I hope to write later this week. After I do that, I will probably want to add to the symmetry article. The role of symmetry in math/physics in general (and gtr in particular) is actually one of my major research interests. One of my goals for many years has been to "popularize" in the physics community the use of packages like GRTensor to compute Killing vectors, optical scalars, Bel decompositions wrt congruences, etc. routinely. I have done this for thousands of exact solutions and have extracted physical insight from such computations on many occasions.

I hope to use the Weyl vacuum and other articles to seque into future articles on multipoles in physics in general and gtr in particular. I also want to write articles on symmetry groups of differential equations, and Lie's "symmetry Ansatz" method of attacking systems of differential equations, including nonlinear partial differential equations.

I also want to write an article on "completely integrable systems", such as the KdV, sine-Gordon equation, and Ernst equation. This topic is closely related to solitons, Bäcklund transformations, SL(2,R) connections (!) in Cartanian geometry (the common generalization of Riemannian and Kleinian geometry), and other beautiful and important (and highly applicable) topics in mathematics.
 * --Chris Hillman

Link added by 82.142.132.74
This anon (the IP seems to be registered to SiberiaEnergougleshab, whatever that is) added a link to http://xstructure.inr.ac.ru. What is this website and what does it have to do with pp-waves? Arin seems to return no information about the domain inr.ac.ru. Who operates it? ---CH 17:27, 10 May 2006 (UTC)

Students beware
I rewrote the June 2005 version of this article, which concerns a topic dear to my heart, and I had been monitoring it for bad edits, but I am leaving the WP and am now abandoning this article to its fate.

Just wanted to provide notice that I am only responsible (in part) for the last version I edited; see User:Hillman/Archive. I emphatically do not vouch for anything you might see in more recent versions, although I hope for the best.

Good luck to all students in your search for information, regardless!---CH 03:01, 1 July 2006 (UTC)