Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gravitational wave equation in FR sapace

  1. Mar 9, 2013 #1
    I am stuck varying an action.
    This is the action [itex]S=\int d^{4}x \frac{a^{2}(t)}{2}(\dot{h}^{2}-(\nabla h)^2)[/itex]

    And this is the solution, [itex]\ddot{h} + 2 \frac{\dot{a}}{a}\dot{h} - \nabla^{2}h [/itex].

    This is what I get [itex]\partial_{0}(a^{2}\partial_{0}h)-\partial_{0}(a^{2}\nabla h)-\nabla(a^{2}\partial_{0}h)+\nabla^{2}(ha^{2})[/itex]
    I don't really see my mistake, perhaps i am missing something. (dot represents [itex]\partial_{0}[/itex])

    It is this problem (see Lectures on the Theory of Cosmological
    Perturbations, by Brandenburger)
    cospert.jpg

    Going from step 91 to 92
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted