The (0,0) and (r,r) components are: [itex]g_{00}= -e^{2\phi}[/itex],[itex]g_{rr}=e^{2\Lambda}[/itex]. From the first component, combined with the fact that the dot product of the four velocity vector with itself is -1, one can find in the MCRF, [itex]U^0=e^{-\phi}[/itex]. What does this mean? In the MCRF, the rate of the two clocks is the same, hence in Minkowski spacetime, U(adsbygoogle = window.adsbygoogle || []).push({}); ^{0}=1. Here, in this case, it isn't so.

From the (r,r) component, one can deduce that if dt=dθ=d[itex]\phi[/itex] =0, i.e the proper radial distance is dl=[itex]e^\Lambda[/itex]dr. Again, what does this mean? In Minkowski space, the proper distance betwenn r_{2}and r_{1}is r_{2}-r_{1}.

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# Metric of a static, spherically symmetric spacetime

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