# A What math do I need to know to understand General Relativity

1. Mar 31, 2016

### Felix Quintana

I'm a 16 year old whose summer goal is two understand general relativity, but I'm lost on what math to have to understand it, I understand topological spaces and a topological manifold. but then it becomes more complicated math, and I know I simply don't understand because of the mathematics.

2. Mar 31, 2016

### BvU

Well, ask on PF and hopefully you shall be assisted....
Preferably specific questions: we can't cough up all kinds of general teaching material; that's what others are for.

3. Mar 31, 2016

### Felix Quintana

So that wasn't a suitable enough question?

4. Mar 31, 2016

### mathman

Differential geometry and anything prerequisite are necessary.

5. Mar 31, 2016

### Felix Quintana

If you could ever be so kind to let me know what are those prerequisites are. It would be very helpful.

6. Mar 31, 2016

### BvU

There was no question in this thread, so I assume you are referring to another thread ?
There are sites that explain special relativity in as simple as possible terms.

7. Mar 31, 2016

### mathman

Calculus and its prerequisites (most high school math).

8. Mar 31, 2016

### Felix Quintana

So linear algebra and differential equations have no need for general relativity?

9. Mar 31, 2016

### BvU

No, but special relativity helps....

10. Mar 31, 2016

### Mondayman

Exploring Black Holes by Wheeler/Taylor is probably the most elementary GR book there is, requiring just calculus and linear algebra. I highly recommend the book Black Holes and Time Warps by Kip Thorne to go along with it.

11. Mar 31, 2016

### Felix Quintana

I have read most of Kip Thorne, I also agree

12. Mar 31, 2016

### micromass

Please tell us in detail what math and physics you know well.

13. Mar 31, 2016

### Felix Quintana

I know Newtonian well, my special relativity iffy, multivariable calculus, some differential equation as in anything first order but can learn more, and currently working on linear algebra and matrix theory. Topological spaces, manifolds. Dabble in abstract algebra( lost intrest after congruency chapter with mod's)

14. Mar 31, 2016

### micromass

If I asked you why all singletons in a Hausdorff space are closed, would you be able to answer me?

How deep do you want to go into the math behind GR? Enough to understand most physics books? Enough to understand Wald and Malament? Enough to understand all the math behind it very rigorously?

15. Mar 31, 2016

### Felix Quintana

Yes! Wald is what I would like to understand for now. I am bored with no more physics available for me to take at my school. Just want to move forward, and general relativity is my next stop on the physics side, but I know my math needs to catch up

16. Mar 31, 2016

### Cruz Martinez

So, how do you prove that singletons are closed in a Hausdorff space?

17. Mar 31, 2016

### micromass

Also, can you explain us why people care about the Hausdorff property? Can you explain why we care about compactness? Why do we let manifolds be second countable?

Sorry, but I want to gauge your topology knowledge.

18. Apr 1, 2016

### Felix Quintana

Oh my fault... I meant yes as in the sense yes for understand wald.... I don't know any of that stuff... Topology I know is the very basics like charting ithe original into a image by taking open subsets of the original and lowering the dimension... Practically the first few pages of wald's book I understand.

19. Apr 1, 2016

### Felix Quintana

So I know relatively close to nothing on topology... Just the very basic... From a set of videos part of a general relativity course on YouTube by something winter school. I can post the link if you'd like.. I know I sound like some ignorant kid messing with something out of his reach, but I insure you I can do it if I'm guided to what I need to know.. I am at the full mercy of all you highly credible geniuses. Thank you

20. Apr 1, 2016

### micromass

Well, the good news is that there are definitely some GR books that you can go through right now, such as Schutz. The bad news that Wald will definitely have to wait for some time until you brush up on your topology and differential geometry. Whethe you are willing to make this investment is up to you.

21. Apr 1, 2016

### PeroK

Do you fully understand Special Relativity?

I'm learning GR from Hartle's book at the moment. I'd say the biggest prerequisite is to have SR nailed. Also, definitely Lagrangian mechanics. Hartle covers both of these, but really only at a revision level.

Obviously knowing classical gravitation helps as well.

I've reached Chapter 9 (Schwarzschild Geometry) and I'd say I haven't needed Topology or Differential Geometry yet. The Differential Geometry has really been what I would call vector calculus.

Hartle, it seems to me, is quite accessible. I'm judging from experience of it alone, but it certainly isn't a mathematical minefield. The only issue is that he gives few hints and no solutions to his problems. But, then, that's where Physics Forums can help!

22. Apr 1, 2016

### ShayanJ

Somebody with a good background in calculus can start reading Zee's Einstein Gravity in a nutshell. It teaches all the math needed in a pedagogic way. But for people who may still think its still advanced for them, Hartle is a good book to start with.

23. Apr 1, 2016

### Felix Quintana

24. Apr 2, 2016

### PeroK

25. Apr 3, 2016

### Cruz Martinez

In addition to the great books that others have recomended to you, I can't keep myself from suggesting you do some pure mathematics aiming at getting a good foundation in the mathematics of GR. This will be very beneficial even if you later on decide you want to do physics only. Trust me, mathematics is beautiful to the extreme, so much that I started trying to learn the math of GR but ended up being more interested in pure mathematics, far more.
There are people on this forum who would really go out of their way to help anyone wanting to learn, have you looked at micromass' signature? I talk from experience when I say he is an excellent teacher.
Anyway, whatever your interests are, I do hope you pursue them. It's great that you have this initiative to learn these subjects.