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Question on General Relativity

  1. Mar 13, 2012 #1
    I'm reading General Relativity by Wald. In chpater 4.4a about Newtonian limit of linearized gravity, it says:
    "When gravity is weak, the linear approximation to GR should be valid. The assumptions about the sources (relative motion << c and material stresses << mass-energy density) then can be formulated more precisely as follows: there exists a global inertial coordinate system of [itex]\eta_{ab}[/itex] such that:
    T_{ab} \approx \rho t_a t_b
    where [itex]t_a=(\frac{\partial}{\partial x^0})_a[/itex] is the "time direction" of this coordinate system."

    I've always thought that
    T_{ab} \approx \rho v_a v_b
    where v is the velocity of the observer (or in other words, the relative velocity between the source and the observer). So, how can I say that
    v_a=(\frac{\partial}{\partial x^0})_a
  2. jcsd
  3. Mar 14, 2012 #2


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    Science Advisor

    That means that the components [itex]v^{\mu}[/itex] of the velocity vector are given by

    v^{\mu} = \frac{dx^{\mu}}{d\tau} \approx (1,0,0,0)

    This is the same as saying

    \frac{dx^0}{d\tau} > > \frac{dx^i}{d\tau}

    which is the non-relativistic limit.
  4. Mar 15, 2012 #3
    Thank you!
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