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

[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!

 

[micromass]

What math do you already know?

 

[HomogenousCow]

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

 

[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?

 

[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".

 

[WannabeNewton]

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

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.

 

[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?)

 

[velixo]

Nevertheless, you really should learn at least lagrangian mechanics before moving on.

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

 

[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?

What are the knowledge requirements of lagrangian mechanics?

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.

 

[velixo]

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?

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?
http://www.physics.rutgers.edu/ugrad/494/bookr03D.pdf

 

[HomogenousCow]

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

 

[WannabeNewton]

Would this PDF be about the classical mechanics you are referring to?
http://www.physics.rutgers.edu/ugrad/494/bookr03D.pdf

No that is more advanced than what I was mentioning. Here is the table of contents from Taylor's Classical Mechanics book: http://www.uscibooks.com/tay2con.htm

 

[velixo]

No that is more advanced than what I was mentioning. Here is the table of contents from Taylor's Classical Mechanics book: http://www.uscibooks.com/tay2con.htm

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