1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Gen. Rel. - Simple tensor stuff

  1. Apr 20, 2007 #1


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    1. The problem statement, all variables and given/known data
    This is a problem that is solved in my course notes, but I don't follow how it's done.

    The problem is to find the general solution to Einstein's equations for a Robertson-Walker cosmology with a stress-energy tensor corresponding to the fluctuations of the void in QFT. This only means that [tex]T_{\mu\nu}=\Lambda g_{\mu\nu}[/tex] where lambda is a scalar.

    So it start with

    [tex]G_{\mu\nu}=8\pi GT_{\mu\nu}[/tex]

    [tex]R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R=8\pi G \Lambda g_{\mu\nu}[/tex]

    And then the next line is

    [tex]R_{\mu\nu}=8\pi G(\Lambda - \frac{1}{2}g_{\mu\nu}T^{\lambda}_{\lambda})[/tex]

    Since when is

    [tex]R=-8\pi GT^{\lambda}_{\lambda}[/tex]

  2. jcsd
  3. Apr 20, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper


    [tex]R^\lambda_\lambda-\frac{1}{2}g^\lambda_\lambda R=8\pi G T^\lambda_\lambda[/tex]

    and [tex]g^\lambda_\lambda=\delta^\lambda_\lambda=4[/tex] and [tex]R^\lambda_\lambda=R[/tex].

    That's since when.
    Last edited: Apr 20, 2007
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook