1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

GR flat and curved space

  1. Feb 13, 2009 #1
    1.a) Concider the 2-space consisting of a spherical shell at constan radius, r. In polar coordinates the line element on the surface can be written (a, b,∈ 1,2)



    2. Relevant equations
    ds2=gabdxadxb=r22+sin2θdφ2
    calculate gab, Γabc, R1212, R2121, R11, R22, R


    3. The attempt at a solution
    I don't have an attempt on a solution cause I honestly have no idea how. Our teacher has said that it's possible to calculate the Christoffel sybols and the metric but he never showd how =/

    really apprisiate any help

    thanks a lot
     
  2. jcsd
  3. Feb 14, 2009 #2
    Well, do you not have any textbook or something where the formula for Christoffel symbol is given in terms of the metric tensor. There is such a formula, and you will need to know it.
     
  4. Feb 14, 2009 #3
    We got the defenition of the christoffelsymbol

    Γrsa=½gal(glr,s+gls,r-grs,l)

    and in flat space gab=(1 0 0 0 || 0 -1 0 0 || 0 0 -1 0 || 0 0 0 -1)

    and R is Riemann's tensor

    I'm supposed to calcuate the same thing for 2-space of the cylinder and then determin which is flat and which is curved, and I know it's the cylinder that is flat and the sphere that's curved.

    And we only have recomended books, we don't need to buy them, and for a poor student like me, well yea, I don't have the money to buy the books.
     
  5. Feb 14, 2009 #4
    Yes, so you have the formula.You can now use it to find all the desired quantities. Similarly for the cylinder you can write down the metric tensor for a cylinder and work it out. I suppose you know the condition for a manifold being curved or not?

    Well, if you can't buy books, there are some online resources. Sean Carroll's lecture notes on GTR are I think freely available. There may be other stuff at a more elementary level, you can look around.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: GR flat and curved space
Loading...