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!

General Relativity, Flat isotropic universe

  1. Oct 13, 2009 #1
    1. The problem statement, all variables and given/known data
    We are looking at an isotropic flat universe, with the metric
    [itex] ds^2 = dt^2 - b(t)^2(dx^2 + dy^2 + dz^2) [/itex]

    I need to write down the energy conservation equation
    [itex] \frac{dV}{V} = -\frac{d\epsilon}{\epsilon + p} [/itex]

    We have been given the solution to be
    [itex] 3\ln(b) = -\int \frac{d\epsilon}{\epsilon + p}[/itex]

    3. The attempt at a solution
    I have found that
    [itex] 3\frac{b'^2}{b^2} = \kappa\epsilon[/itex]
    by solving the [itex]{}^t_t[/itex] component of the Einstein Equation
    [itex]R^a_b -\frac{1}{2}R\delta^a_b = \kappa T^a_b[/itex].
    [itex] b' = \partial_t b[/itex], and [itex]\epsilon[/itex] is the energy density, after having found the Christoffel symbols, Riemann tensor, Ricci tensor and Ricci Scalar.

    I can't seem to find an equation of V or dV.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

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



Similar Discussions: General Relativity, Flat isotropic universe
  1. General Relativity (Replies: 4)

Loading...