Gotta be somebody

I finally got a reply from my prospective supervisor for my PhD. By the looks of the email I think he may have already though he spoke to me about a PhD because he gave me a list of possible project ideas. So I have to have a look at them and write a short research proposal asap.

1. spherical EYM with non-vanishing electric fields (SSEYMe)

2. spherical massless scalar field (SSEMSF) - are the critical solutions
singular?

3. Quasi-local mass with matter (Maxwell, YM coupling etc)

4. geometry and applications of spherical coordinate choices for space-time


He also commented that topics 1 and 2 would have a substantial computing aspect, 3 would be rather geometrical and 4 would be more of a review and he said it "would be marginal but could suffice". I think that rules out 4. These are just ideas though so I'm free to start with anything in between and outside (to a degree) and then let it change into something completely different over the first year.

3 leaps out at me as extremely interesting so I'm going to hopefully do some reading on that today and tomorrow and hopefully write my research proposal on that.

For those interested; Local mass/energy in general rel is something that still isn't well defined because if you take some area of space and ask the question 'how much energy is there in this area?' there is no clear cut way of answering it. A major problem is that there is gravitational contributions via the curvyness of space-time which is a global property. There have been several (less than 10 though) definitions of a local mass in G.R. which usually are either impossible to practically calculate or have flaws such as admitted negative mass or adding two things together and getting less than both individual masses or they only work for particular regions such as spheres. The reason I would think looking at mass would be good because my supervisor defined one (impossible to calculate though) in 89 which often pops up when you looks for anything to do with mass in G.R. Other people who have defined such masses include Hawking and Penrose who I'd hope most people have heard of.

(This paragraph also for the interested.) The incorporation of matter into the mass I think (based on the content in parenthesis) is that he wants to look at coupling Yang-Mills gauge theories to G.R. and try to make a mass definition still work. This bit is quite unclear to me right now though. Yang-Mills gauge theories are rather strange geometric interpretations of fields (or matter).


Back down to earth now...

Read this. Quite entertaining, especially reading the quotes.
http://news.ninemsn.com.au/article.aspx?id=651937