Dear fellow relativiters,(adsbygoogle = window.adsbygoogle || []).push({});

I never fully got how to get from the field equations of Einstein's

[itex] R_{ \mu \nu} - \frac{1}{2} g_{ \mu \nu} R= -\frac{8 \pi G}{c^4} T_{ \mu \nu} [/itex]

to a special metric, let's say the FRW metric

[itex] ds^2 = c^2 dt^2 - a(t)^2 \cdot (\frac{dx^2}{1-kx^2} + x^2 d\Omega^2) [/itex]

and from there the equation of motion for a particle facing gravitational force.

In the above I left out [itex] \Lambda g_{\mu\nu} [/itex] the term that represents that the metric itself is a solution and that gravity is repulsive on scales of vacuum energy.

So in Newtonian approximation I should get something like the inverse square law + [itex] \Lambda \cdot \vec{r} [/itex] ?

Thanks

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# From field equation to equation of motion

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