Background required for general relativity

[khil_phys]

I've completed college-level special relativity, which includes length contraction, time dilation, the Lorentz transformations, momentum and energy. What additional mathematical and physical knowledge do I need for starting to read general relativity?

 

[haushofer]

Newtonian mechanics is more or less required, as GR extends the Newtonian ideas. Mathematical prerequisites are the usual analysis, linear algebra and stuff like that. The main language of GR is differential geometry (tensors, manifolds, etc.)

You could take a look at Sean Carroll's notes about GR to get an idea :)

 

[Naty1]

Lots of people have interpretated the complicated/detailed mathematics of general relativity so you can read those expert interpretations instead of studying all the precise math to get started.



Here are some sources I've found helpful:

Carroll’s lecture notes:http://xxx.lanl.gov/abs/gr-qc/9712019
http://www.mathpages.com/rr/rrtoc.htm
http://www.lightandmatter.com/html_books/genrel/

You can also check online for MIT and Caltech lectures.

For some advanced stuff introductions, take a look at some diagrams in wikipedia for Schwarzschild,Kerr and Rindler coordinates/metrics.

Inexpensive books:
An introductory paperback, half special and half general relativity is RELATIVITY SIMPLY EXPLAINED by Martin Gardner...no math, maybe too simple if you have studied special relativity in college.

A paperback book I found useful, and it goes into math in later sections, is Peter Bergmann THEORY OF RELATIVITY...Bergmann was a student of Einstein...and also by him
THE RIDDLE OF GRAVITATION which is excellent...and has a bit on quantum mechanics.

An advanced book is GENERAL RELATIVITY,ASTROPHYSICS AND COSMOLOGY by Raychaudhuri...it's pretty difficult, a graduate level study..all math...too much for me.

finally: read discussions in these forums...keep notes of things that interest you.

 

[mathman]

The major additional mathematics needed is differential geometry.

http://people.hofstra.edu/Stefan_Waner/diff_geom/tc.html

 

[khil_phys]

An introductory paperback, half special and half general relativity is RELATIVITY SIMPLY EXPLAINED by Martin Gardner...no math, maybe too simple if you have studied special relativity in college.

I'm not yet in college, so there's no question of someone having taught it to me. I studied it from college texts, and picked it up nicely.

But, I do lack the mathematical sophistication for GR. Can you suggest me some math texts for it, so that I can get started?

 

[Daverz]

Understanding the full Einstein Field Equations (EFE) requires quite a lot more work. However, you can still learn a lot without this full machinery if you take the solutions to the full EFE for the spherically symmetric case "on faith". See for example the texts:

Taylor & Wheeler, Exploring Black Holes
Hartle, Gravity

 

[khil_phys]

"On faith" is not where the fun lies. I would like to learn it systematically, without skipping out the math.

 

[harrylin]

"On faith" is not where the fun lies. I would like to learn it systematically, without skipping out the math.

You could, just like Einstein, start with the equivalence principle and basic mathematics, and verify what has been deduced from that. Perhaps you would not call that "systematic", but it's certainly not "on faith".

 

[Polyrhythmic]

I always thought that GR was background-independent...