# I want to learn general relativity

1. Nov 14, 2014

### dumbperson

hello,

I would like to learn general relativity.

To understand general relativity, do I need to understand the math on a rigorous level? (the way mathematicians understand the math) . What math do I need?

Can you suggest me some math/general relativity books?

Thanks and sorry if my english is bad!

2. Nov 14, 2014

### phinds

Yes, you will need to study at least several years worth of math, possibly more depending on where you are now. Others here who know more than I do will give you the details, but it has been posted here several times before so I suggest a forum search.

3. Nov 14, 2014

### Matterwave

It depends on what you mean when you say you want to "learn general relativity". If you want to learn it as a physicist would learn it, you need to learn quite a bit of math, including all the standard mathematics required for other physics topics such as algebra, geometry, single and multi-variable calculus, linear algebra, and differential equations (ordinary differential equations as well as partial differential equations). Beyond the basics, you will also have to have a good grasp of differential geometry, and it would be good to know a little bit of basic topology.

You could just learn what the theory of general relativity is, though, without understanding the math very much. You just wouldn't be able to do any calculations or understand the underlying mathematical structure. But you can learn about the phenomenology of general relativity (e.g. that it predicts black holes, or that it predicts gravitational time dilation) without need for so much math.

4. Nov 14, 2014

### dextercioby

And for that the OP can simply read Dirac's <80 page booklet from 1975. :) Dirac, just as other quantum physicists such as Pauli, Weinberg and Feynman, wrote texts on GR without the emphasis on differential geometry.

5. Nov 15, 2014

### dumbperson

I want to learn it as a (mathematical) physicist would learn it. I know all the math you mentioned except differential geometry and topology

6. Nov 15, 2014

### Matterwave

Oomph, if you want to learn it as a mathematical physicist, then you better get a good foundation in topology and differential geometry. A regular physicist would probably be able to get away with just learning these topics from a GR book, since most GR books will not presume a prior knowledge of such topics and go over them a little bit, but a mathematical physicist should learn these topics in some detail so as to better understand the geometrical nature of GR. I think Nakahara is a pretty standard reference for such an endeavor.

7. Nov 15, 2014

### Daverz

You do need a practical understanding of the math and physics. Math through vector calculus, linear algebra, and differential equations and physics through mechanics and E & M.

This question also comes up rather often here, so you should do a search back through older threads like: