# What concepts/subjects do I need to understand General Relativity?

1. Apr 26, 2013

### velixo

I am a high school student. I looked up Special relativity and grasped it pretty easily, without needing to learn any new math. But when I tried to read about general relativity, I was immediately confused by all the math, equations and notation. My problem is that I have no idea where to begin to progressively learn about general relativity. So I would really appreciate it if you could advise me on what (mathematical) topics to look up on before I continue, and preferably in order (for example learn topic 1, then topic 2, etc). Thanks in advance!

2. Apr 26, 2013

### micromass

What math do you already know?

3. Apr 26, 2013

### HomogenousCow

You need a solid understanding of linear algebra, tensor calculus and differential equations.

4. Apr 26, 2013

### velixo

I know things up to basic calculus: stuff like derivates, integrals, rotating integrals, differential equations. Trigonometry, if that counts as calculus (I live in sweden so I don't exactly know what americans consider calculus)

Just a question: do Lagrangian or Hamiltonian mechanics play a part in General Relativity?

5. Apr 26, 2013

### WannabeNewton

Learn classical mechanics and electrodynamics before you start learning the *physics* of GR. I'm only saying this because I started learning GR in junior year of high school but I can tell you now that taking a hiatus midway and solidifying the stuff I just mentioned above before jumping back in senior year paid off greatly.

If you learn classical mechanics, electrodynamics, calc 3 (multivariate), and linear algebra then you can start learning from an undergraduate intro text like Hartle's "Gravity".

6. Apr 26, 2013

### WannabeNewton

An introductory text usually won't go into variational principles for the field equations of GR (e.g. Hilbert action / Palatini action) nor into the Hamiltonian formalism. Nevertheless, you really should learn at least lagrangian mechanics before moving on.

7. Apr 26, 2013

### velixo

For classical mechanics, I've learned about:

Forces, pressure, Newtons laws, momentum
Energy (kinetic and potential)
Thermodynamics
Electricity and Magnetism
Optics
Waves (sound, spring and light - although light is more about quantum mechanics?)

8. Apr 26, 2013

### velixo

I tried looking at lagrangian mechanics but I got lost at the introduction :P What are the knowledge requirements of lagrangian mechanics?

9. Apr 26, 2013

### WannabeNewton

When I said classical mechanics and electromagnetism I meant like at the level of Taylor and Griffiths respectively. For example, if I asked you what $\nabla\times E = -\frac{\partial B}{\partial t}$ meant physically, would you be able to answer?

Here in the US, people usually learn lagrangian mechanics in 2nd year mechanics classes so basically, at the bare minimum, after a year of introductory calculus based physics and some multivariable calculus. If lagrangian mechanics is confusing to you at this present moment then I would say put off learning GR before you have your mechanics solidified.

10. Apr 26, 2013

### velixo

I kinda understand it, I've seen some videos on Khanacademy about divergence and curl (don't remember which one that triangle symbol is referring to ) and partial derivatives, but I haven't seen them used in physics. Would this PDF be about the classical mechanics you are referring to?

11. Apr 26, 2013

### HomogenousCow

You also need to master SR in tensorial formulation first, or else it will be a haze of greek subscripts and superscripts.

12. Apr 26, 2013

### WannabeNewton

13. Apr 26, 2013

### velixo

Thanks a whole lot, this seems very useful! Can't thank you enough :)