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Getting the Ricci and metric tensor from T ?

  1. Jul 10, 2009 #1
    Okay, we have Einstein's field equation:

    R_ab + 1/2 R g_ab = 8pi T_ab

    Let's say we have T_ab defined for some region of space, and we want to calculate the spacetime from that. How would you calculate R_ab, R and g_ab? Supposedly you can write it as a system of PDEs but I cannot find them anywhere!

    I'm just starting to learn GR, if I could see how you'd put it in a computer to solve them it would help me "see" it better. Thanks.
     
  2. jcsd
  3. Jul 10, 2009 #2

    malawi_glenn

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    But it all depends on who T_ab looks, there is no "general" solution to ALL.

    The easiest solution is obtained by T_ab as static (no timedep.) and spherical symmetric, that solution for the metric is called the Schwarzschild metric.

    http://en.wikipedia.org/wiki/Schwarzschild_metric
    here is an outline of it's derivation:
    http://en.wikipedia.org/wiki/Deriving_the_Schwarzschild_solution

    I mean HOW to solve it depends from case to case, you are just after the form of the PDE's? But that is trivial to find, just plug in whatever you have for the Ricci tensor and Ricci scalar in terms of the metric (your multidimensional function which depends on several variables)
     
  4. Jul 10, 2009 #3
    Okay, how do you calculate the Ricci scaler and tensor in the first place then?
     
  5. Jul 10, 2009 #4

    malawi_glenn

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  6. Jul 10, 2009 #5
    Just learning it on my own. I have Wald's GR right now, I'm getting Einstein's populist book and GR A to B soon thru ILL hopefully.
     
  7. Jul 10, 2009 #6

    malawi_glenn

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    ok cool!

    But how come you asked about solutions to Einsteins equation if you don't know how how ricci tensor and ricci scalar is related to the metric?... I strongly recommend to study in logical order :-)
     
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