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

  1. Apr 26, 2013 #1
    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!
     
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  3. Apr 26, 2013 #2

    micromass

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    What math do you already know?
     
  4. Apr 26, 2013 #3
    You need a solid understanding of linear algebra, tensor calculus and differential equations.
     
  5. Apr 26, 2013 #4
    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?
     
  6. Apr 26, 2013 #5

    WannabeNewton

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    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".
     
  7. Apr 26, 2013 #6

    WannabeNewton

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    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.
     
  8. Apr 26, 2013 #7
    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?)
     
  9. Apr 26, 2013 #8
    I tried looking at lagrangian mechanics but I got lost at the introduction :P What are the knowledge requirements of lagrangian mechanics?
     
  10. Apr 26, 2013 #9

    WannabeNewton

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    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.
     
  11. Apr 26, 2013 #10
    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
     
  12. Apr 26, 2013 #11
    You also need to master SR in tensorial formulation first, or else it will be a haze of greek subscripts and superscripts.
     
  13. Apr 26, 2013 #12

    WannabeNewton

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  14. Apr 26, 2013 #13
    Thanks a whole lot, this seems very useful! Can't thank you enough :)
     
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