A Course Plan to Master General Relativity

[aLearner]

So this is purely for self-study purposes. Say I'm very keen on understanding GR well, but I don't even have the prerequisites done for even starting to grasp GR. Would anyone be able to give an outline of the skills necessary in understanding GR?

An outline would look something like this

Basic Math
Calculus
Classical Mechanics
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First General Relativity Book
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Advanced math or something
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Time to do research in GR

So basically what skills do I need to acquire in order to fully comprehend GR, and how much of those skills do I need (a little = nice to know, but can get by, a lot = should know to understand well, but can get by difficultly, tons = must know like the back of your hand)

I'm trying to make a little check list for anyone who is interested in pursuing the topic.

 

[ZombieFeynman]

Beyond calculus, a firm grasp of non euclidean geometry is necessary. Vector and tensor analysis. Electrodynamics and special relativity for some context.

 

[dextercioby]

It's very difficult to learn a theory by yourself, only with the help of the textbook (and perhaps some Physicsforumers to answer your questions), but it's worth a shot. There are approximately 100 textbooks/treatises to cover the subject, at various levels of mathematical involvement. And 1000 textbooks for the normal prequisites, both on the maths side (calculus, differential geometry both of them requiring minimum knowledge of set theory and topology) and on the physics side (Newtonian dynamics, Newtonian gravity, electrodynamics, special relativity, Lagrangian dynamics).

Depending on how far you may want to go, you may call yourself <knowledgeable of GR> only if you're comfortable with differential geometry.

 

[aLearner]

Well, so after some internet searching, this is what I got.

Calculus 1,2,3
ODEs
Linear Algebra
Introduction to Classical Mechanics
Introduction to electrodynamics

A General Relativity Workbook Thomas A. Moore
Introduction to Tensor Calculus, Relativity, and Cosmology Lawden
Tensor Calculus Synge and Schild's
The Principle of Relativity Einstein
A First Course in General Relativity Schutz
Advanced General Relativity John Stuart
Mathematical Problems of General Relativity Zurich Lectures

so 7 actual GR books which cover the math to prepare someone to get into GR

 

[bcrowell]

GR can be studied at a lot of different mathematical levels. There are no math prerequisites. A good book that uses very little math is General Relativity from A to B by Geroch. A good book that uses only simple calculus is Exploring Black Holes by Taylor and Wheeler. Post about what math you have *now*, and we can talk about what GR you can learn, or what math you could learn next to understand GR at a deeper level.

 

[aLearner]

GR can be studied at a lot of different mathematical levels. There are no math prerequisites. A good book that uses very little math is General Relativity from A to B by Geroch. A good book that uses only simple calculus is Exploring Black Holes by Taylor and Wheeler. Post about what math you have *now*, and we can talk about what GR you can learn, or what math you could learn next to understand GR at a deeper level.

Well I can do single and multivariable calculus. I know some ODES and a little abstract algebra. Oh, and I know some linear algebra. especially square matrices and transformation matrices that I had to learn for a robotics read. I would really like to get advanced level math for GR, because I hope to work on GR over the summer (that gives me time till June).

 

[bcrowell]

Well I can do single and multivariable calculus. I know some ODES and a little abstract algebra. Oh, and I know some linear algebra. especially square matrices and transformation matrices that I had to learn for a robotics read. I would really like to get advanced level math for GR, because I hope to work on GR over the summer (that gives me time till June).

The math you already know is all you need in order to tackle a graduate-level GR book. Those books teach you the additional math you need, such as tensors and noneuclidean geometry.

But what is your background in *physics*? GR is a classical field theory, and it's a much more difficult field theory than E&M. You need a solid background in E&M (preferably at the level of Jackson) before attempting GR at the level of a graduate text.

 

[Sonderval]

You could also do it the other way round:
Grasp a GR book that looks good to you (in my opinion, Misner Thorne Wheeler is quite good for an introduction and has many pedagogical aids) and when you get stuck at some point, acquire whatever you need to get on. This has the advantage of you staying focused on your goal (learning GR) and also that it is a way of approaching a new problem that you will often encounter later (you find a paper you need to understand get stuck at some point, read up references, continue a bit until the next problem etc.).

 

[aLearner]

You could also do it the other way round:
Grasp a GR book that looks good to you (in my opinion, Misner Thorne Wheeler is quite good for an introduction and has many pedagogical aids) and when you get stuck at some point, acquire whatever you need to get on. This has the advantage of you staying focused on your goal (learning GR) and also that it is a way of approaching a new problem that you will often encounter later (you find a paper you need to understand get stuck at some point, read up references, continue a bit until the next problem etc.).

well I've started on bcrowel's plan because a strong foundation in E&M is always helpful. Besides, if I can kill intro E&M and advanced E&M during the same semester, that says something. But I'll probably practice your advice once I get into the actual GR part of the project (hopefully 2 or so months in the future).