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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:

[tex]

T_{ab} \approx \rho t_a t_b

[/tex]

where [itex]t_a=(\frac{\partial}{\partial x^0})_a[/itex] is the "time direction" of this coordinate system."

I've always thought that

[tex]

T_{ab} \approx \rho v_a v_b

[/tex]

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

[tex]

v_a=(\frac{\partial}{\partial x^0})_a

[/tex]

?