Undergrad GR

[Royston]

This question is to anyone who's studying / studied a physics degree. I'm covering SR in a couple of months, so I decided to look through my future courses on studying GR (undergrad.) It seems to be pretty basic, infact a huge bulk of differential geometry isn't covered until the Master (postgrad) math courses...I typed in tensor into the prospectus search, and no results came up !?!

 

What is covered of the Einstein equations seems to be lacking the mathematical background you need to fully understand the equations.

 

Is this right ? Are you only expected to understand GR fully at post-grad level and further ?

 

EDIT: Having another look, our post-grad courses seem pretty thin on the ground with regards to physics, but I was thinking of doing my Masters full-time (obviously depending if I do well in my degree) however, I was still a little dissapointed with the cursory study of GR at undergrad...is this the same for most Uni's ?

[Klaynos]

We have a 4th year optional course (well require if you're a MPhys astro person) but it's taught by someone who I'd rather not be taught by, I don't like his style, so I didn't take the course.

 

That seems to be pretty standard...

 

I think we discussed it shortly in our second year relativity course but only applications of it, we didn't actually do any maths.

[abskebabs]

Hi Snail, I think to a broad extent you're right, but I think what you're talking about extends beyond just General relativity(I think QM is another great example of this). I'm in my second year and we finish having a stand alone maths module this year, the rest I think is taught "on the go" in a way, though we do have specific modules dedicated to things like PDEs and specific maths. As for SR, I covered it twice in the 1st year and the treatment was basic in one module, and more complete in the other, doing as much of relativity you can do without properly invoking linear algebra and tensors(because we hadn't been taught it yet).

 

I asked one of my lecturers concernign the maths involving general relativity and he said as we also have a relativity module in the 3rd year, the whole linear algebra/ tensor and geometry approach to it is built up in that year. This is before the course on GR in the 4th year. So, I guess my answer is yes, we do have a GR course in the 4th year at Birmingham, it's compulsory for me because I do Theoretical Physics. Not sure how cursory it is yet, but I'd like to think it isn't very...

 

On a separate, but related point I think we don't get taught enough maths in our school system, so that when it comes to uni, most of the early maths is just catching you up with what undergraduates in the past already knew. Saying this however, I must admit I am a product of the British education system myself, and I chickened out from taking further maths at A level:doh:.

[ajb]

My undergraduate experience of general relativity was pretty poor. Most of the emphasis was on calculating rather than having any understanding.

 

You really do need some differential geometry to understand GR in any real sense. So, I would agree with you that postgrad study in GR and differential geometry is needed. if you want to understand GR.

[abskebabs]

I typed in tensor into the prospectus search, and no results came up !?!

I guess this may depend on your prospectus search engine, but not even the inertia tensor came up? That should be covered as that's CM. Also I'd think any respectable later year course on EM should have tensors too.

[CPL.Luke]

my GR course spent the first two months covering math, and then we spent the latter two months studying the schwarschild solution and the basics of cosmology.

 

honestly I don't feel as if I have that good of grounding in it, for that I think I'll have to wait another few years for a grad course, but it covered enough math and such so that we could appreciate what the equations meant and how to work with them in general.

 

 

for things like QM and such there is a better sense of understanding when you finish it. although this varies person to person, for instance while I feel I have a very good understanding f the qm I was taught (griffiths, and now merzbacher) my current EM course feels more like there isn't much understanding, although I'm sure there are others who feel the opposite.

[Royston]

I guess this may depend on your prospectus search engine, but not even the inertia tensor came up? That should be covered as that's CM. Also I'd think any respectable later year course on EM should have tensors too.

 

It's possibly the search engine, tensors came up in one of the engineering courses, but I'm obviously more interested if they're included in the material I'll be covering...which didn't come up with anything. However, I can't believe they're not covered somewhere, so I'll wait and see.

 

honestly I don't feel as if I have that good of grounding in it, for that I think I'll have to wait another few years for a grad course, but it covered enough math and such so that we could appreciate what the equations meant and how to work with them in general.

 

This was the impression I got when reading through the cosmology (mainly GR) course I'll be taking. It's ok, but not going into the depth I was hoping for...as I'm looking at postgrad cosmology (subject to change) I'll have to get up to speed by doing some outside study.

 

Thanks all for the responses

[CPL.Luke]

it went into enough depth that there wasnt anything important that I felt I missed, however it would be necessary to do more problems in it in order to better appreciate it.

[ajb]

If you want reference for general relativity I suggest

 

1)Wald, General Relativity. This book really pushes the need to understand differential geometry and indeed tensors!

 

2)Dirac, General Theory of Relativity. Far Less mathematical rigour or understanding, but is shows calculations in good detail.

 

3)Carroll, Spacetime and Geometry: An Introduction to General Relativity. I have not used this book, but if it is any think like the lectures notes it will be good.

 

4)Nakahara, Geometry, Topology and Physics. Not a book on GR as such, but in the chapters on differential geometry, general relativity is discussed. Quite clear on spinors in GR. A must if you want a introduction to geometry in physics.

 

5)Bertlmann , Anomalies in Quantum Field Theory. Again, not really a book on GR, but again it discusses the geometry needed for GR and quantum field theory in a nice way. It also discusses the first order formalism of GR.

[Royston]

Thanks for the suggestions, ajb. I've bookmarked this page for future reference. The Wald, Bertlmann and Nakahara books, certainly sound like the material I'm looking for.