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: Gauge Transformations in GR

  1. Nov 14, 2013 #1
    I need some help with a derivation in GR.

    The linearized field equation in GR is:

    [tex]G_{ab}^{(1)} = - \frac{1}{2}{\partial ^c}{\partial _c}{{\bar \gamma }_{ab}} + {\partial ^c}{\partial _{(b}}{{\bar \gamma }_{a)c}} - \frac{1}{2}{\eta _{ab}}{\partial ^c}{\partial ^d}{{\bar \gamma }_{cd}} = 8\pi {T_{ab}}[/tex]

    How would I use the gauge transformation

    [tex]{\gamma _{ab}} \to {\gamma _{ab}} + {\partial _b}{\xi _a} + {\partial _a}{\xi _b}[/tex]

    to simplify the linearized equation to:

    [tex]{\partial ^c}{\partial _c}{{\bar \gamma }_{ab}} = - 16\pi {T_{ab}}[/tex]?

    EDIT: I should also mention:

    [tex]{{\bar \gamma }_{ab}} = {\gamma _{ab}} - \frac{1}{2}{\eta _{ab}}\gamma [/tex]

    [tex]\gamma = \gamma _a^a[/tex]


    [tex]{g_{ab}} = {\eta _{ab}} + {\gamma _{ab}}[/tex]
  2. jcsd
  3. Nov 16, 2013 #2
    Nvm. I figured it out.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted